Merchant party doesn't like you having weapons in your hand. No idea why, it's just so. The reason they didn't warn you or shoot at you sooner was because they were preoccupied with whatever critters they were fighting at the time. Normally they warn you first.
Science is good for several things. When dismantling items, a higher science skill gives you more materials. It's also good for several perks, namely Dismantler, Educated and Swift Learner. And of course, the Energy Expert profession. If your character crafts, it's not a waste.
Doc and First Aid are good to have, and yes... it's worth putting them to 100. The higher the skill, the lower the cool down for using it. With First Aid you also heal more HP the higher it is, in addition to the reduced cool down. Doc works similarly, but instead of healing HP it heals crippled or injured body parts, and 100 is usually good to have.
Having a 1 LK character with the two extra critical perks isn't normally something that is done. Spray and Pray only affects un-targeted shots, and 16% crit chance is a bit low to really get the effectiveness out of that perk.