Hello and welcome to the forum.      Enjoy

If when you wind the watch the train wheels spin as @caseback mentioned check the escape wheel pallet engagement and also the engagement of the other train wheels, you may have one upside down . Did it work ok before you worked on it.

Hi. There are dos and donts with these clocks, the alignment dots on the strike train and also on the front work, minute wheel , intermediate wheel and the hour wheel must also align, I have not found any definitive text regarding alignment but reference to them are usual found in books  by Mike Watters, Laurie Penman, and Donald De Carle and iam sure many others. It’s a question of reading up on the subject and making your own notes for future reference.

The clickspring is not the problem. When the power is released, the barrel turns. That should not happen. The pallet fork should be blocking the train of wheels while you're putting some wind in. Try again and focus on how the pallet fork and the escape wheel interact.  

Timex stems were not threaded - the stem and crown were shipped as one part, firmly friction fit together. The grooves you see are part of that friction fit. It is likely that if you just put some blue Loctite in the crown and press the stem into it that it will hold and work correctly. Since this is a Timex, I would not shy away from super gluing the crown to the stem either. What might have happened here is someone tried to replace the crown but expected it to be like a normal threaded type and damaged the stem or crown or both. It is unfortunately difficult and expensive to find correct replacements for these stems and crowns because you need to know the right part for the case design (as published in the Timex parts books) and then get access to a stash of NOS parts which are pretty uncommon. If you find the right one, sellers will usually be asking upwards of $30 for it and the watches are rarely worth it unless they have sentimental value or high collector value.