so that 100 pound ball really was a dragonball. Too bad I died. Very shortly after finding it, in fact.
Yes. Dragonballs are a trap that kill a lot of new players. Speed is a huge factor in character survivability because it not only controls movement speed relative to monsters, it also indirectly affects number of attacks everyone gets. If you pick up a dragonball and get hit with -12 speed, that means that a monster with a base speed can not only move over twice as fast as you, it means that once they're standing next to you they'll hit you twice per turn, except every fifth turn when they'll hit you three times. For example...with a little bad luck, you might get thrown by a black belt next to two brown belts. Quick check of monster stats, brown belts have a speed of +10. So with a -12 speed, it would be possible for them to each get three attacks to your one. 1d8 damage, so theoretical worst case, those two brown belts might hit you for 48 damage before you even get to move. Playing with negative speed is suicide.
If you find an early dragonball and you don't have a house...my advice is to abandon it. If you just leave it on the ground in any non-persistent map then leave, it can respawn again later.
apparently I can get a house by being a technomancer instead of marriage
...if I remember this correctly...there are two options here. If you marry Buruma you get a house accessible form the world map just like the Oolong marriage house. If you become a technomancer (explained below) you gain item pickup and drop access to Dr. Brief's lab. So the "technomancy house" is different than the standard marriage house, but in a way it's better, though less organized since you have to physically move around and sort through piles to get what you want rather than choose from a list like in a house.
Speaking of Technomancers, how does science relate to weapon difficulties, if at all?
Other classes have skills that help them hit better, but I'm
not sure if technomancy in and of itself helps.
Technology provides no hit bonus. It's not a combat skill.
As for "how it helps" we need to distinguish between technology skill and a full blown technomancer. Technomancy is a character class archetype. Technology skill just allows you to use tech items. General consensus amongst old school DBT players was that technomancers were viable, but sort of middle of the road in terms of power.
Think of it this way: DBT characters are defined on two axes: basic method of damage dealing (barehand, weapons or firearms) and "super powered enhancement" of which the choice is either chi or technology. You get get through the early game just by picking some combat styles and smashing your way through everything. But late game, if you want to be able to fly, to heal yourself, to travel through space to other planets, if you want to be able to deal with traps of bleed effects...you need either chi or technology to do it.
Low levels of technology skill will give you access to a lot of tools that enhance your survivability and generally make the game easier: laser pointers, metal detectors, the dragon radar, etc. Also a lot of misc stuff with combat utility: road flares, flame throwers, etc.
Next, there are a number of weapons that can only be used by characters with technology skill: tasers, stun batons, cattle prods, etc. While the above examples are usable by anyone with enough technology skill, weapons in this category require technology skill but actually use your weapons skill for to hit rolls. This is why most technomancers go weapons rather than barehand. (Or firearms, but they're bugged in your version.)
Finally...the "mother lode" is when you actually become a dedicated technomancer, which is a quest-chain driven event that becomes available by speaking to Dr. Briefs after you reach a technology skill of 20, and provided you haven't done anything especially nasty to Buruma. After completing the quest chain your class title changes to "Technomancer" and you gain the ability to create and enhance
items via a disenchant/enchant mechanic. When you disassemble an item of a given ego or base type, you can learn how to make those items and/or apply that ego type to other items. So, for example...if you disassemble a studded piece of body armor, you can then apply studding to any suitable piece of armor you find from then forward. If you have only one stun baton, but two hands and the ability to dual wield, you can disassemble the stun baton to learn the recipe and build two to dual wield them. Then apply, for example, the high voltage ego type to them so they do additional stun damage. This allows you to always have the best "enchantments" on your gear. While one character who might be terribly dependent on armor, for example...might find himself in the position of having to choose between a piece of armor with low armor but good resistance values, a technomancer will just enhance the better piece of armor with the bonuses he wants.
Also, as a minor side benefit, technomancers get free use of a couple items that other characters would have to spend skill points to be able to use like motorcycles and airplanes.
It was also in the works to have technomancers be able to build upgradable power armor similar to what you see in bubblegum crisis. But that system was never finished.
Anyway, technomancy is somewhat crippled in the version you're playing because ego items don't spawn, so you'll have far fewer items to disassemble in order to learn recipes and you'll be completely dependent on blueprints for learning ego types. (Though I suppose that might be better than not being a technomancer and therefore not having access to ego items at all.)
So there you go. Technomancy is an alternative to chi training for late-game special abilities. But, even if you don't want to go full-on technomancer, an easy 5 or so points in technology skill is enough to allow you to use a lot useful items. Much past Mr Satan's estate, simply pouring points into armor and damage won't be enough to keep you alive. You'll need trap mitigation, healing, a way to deal with and dish out stun and blindness effects, etc. Technology training is easier to gain access to in the early game since all you need to do is find Buruma rather than navigate through mid to high level zones in order to get to chi trainers.
how to I avoid/counteract throws?
If you want to become immune, the easiest method is to train sumo and learn the immovability trait. Body oil provides temporary immunity that lasts about a dozen turns (depending on speed) and is available for sale to anyone from the sumo school.
If you want to gain the ability to maneuver yourself better, there are lots of options: the jump ability to dance, chi flight and/or teleportation, the Nyoi-bo artifct from the Uranai-Baba quest chain...or even just train speed a lot. It doesn't matter as much when they throw you around if you can just run around them to where you want to go an hit them 2-3 times for every once they hit you.
Note that if the problem is that you're being thrown from the ring in the world tournament, the Nyoi-bo counts as a tool and will disqualify you.
Also, I hate Lunch
I think in the version you're playing she's able to spawn anywhere. That was not the case in later versions. She's a level 15 unique. She's only supposed to spawn in mid-level overworld zones.
Workaround: when you see the sneeze notifications, leave the area and come back. I'm pretty sure Yamcha and Puar are the only hostile overworld uniques who persist through refreshes.