Why does my gear slip when putting it into first and third

Sounds like the synchro mesh has worn out

Problems such replacing or adjusting clutches, replacing or adjusting bands, and replacing gears will require you to dismantle the transmission. IF your fluid smells burnt or is brown/black it is from overheating. Changing it may solve some slippage but maybe not. Short version: you need the tranny overhauled. Don't waste $$$ on the fluid change, Rebuilt transmissions can gave several year long warranties, and can include labor so check round.

According to Autos.com: " Fixing common transmission slip problems is easy once you have determined the cause. If you notice that there is low automatic transmission fluid then all you need to do is fill it with enough fluid to allow the transmission to work properly.
If there are any worn out parts like the transmission gear or a defective shift gear, it is important that this is replaced as soon as possible. In some cases you may just need to readjust the shift gear instead of replacing it entirely. In the event that the transmission bands are worn out, just replace the worn out bands to fix the problem."