OK, I'm new to the game, bought it this week.
So far, I'm pretty satisfied with it, but I have a question.

Do repair kits exist in the game? If so, where can I get one?

I looked up the ATOM fandom wiki and several crafting items require a repair kit. One quest, Rescue The Mechanic, said that a repair kit would become available once he's back in Otradnoye, but he doesn't have a Barter option.
In the wiki, I've noticed that tool kits are not linked and I'm wondering if they've been edited out of the game or something.

Hi there,
this is strange,in my game,after rescuing him,the mechanic HAD a toolkit to buy.But don't worry,there are some of them to buy from caravan-merchants or in other towns.It is very hard to pay him off early,the toolkit was over 1000 rubels for me and crafting skills aren't high enough at the start for the recipes with a toolkit,except you force build a crafter.
So take it easy,and don't spoil your fun by reading the recipes on WIKI that much,try them out for yourself,it is much more fun that way!

Enjoy the game!

Armor and weapons do not deteriorate, so "repair kits" do not exist. The Mechanic you need to rescue does carry a "Toolbox", wielding this tool grants you a +30 for tech. But repairing the water pump shouldn't require such a high tech level any way. Barter screen should be the bright yellow/white button when talking to him after the rescue.

I reckon by now the issue from your post has long been solved though :P

Personally I actually found that I can get a better price for the repair kit from one of the vendors in Krasno than what the mechanic charges me. When I first got the game it was the other way around - however since the massive update to the Dead City (possibly before?) the Krasno guy was cheaper. Not sure if it was related to how I treated him or not...