Tacoma

I have three issues with my 2007 tacoma hopefully someone can help me figure them out!
1. when i am going over any big bumps or rocky roads I can feel movement in the steering wheel and makes a thud noise every bump
2. when I put my truck in drive as soon as I start it up and turn the steering wheel there is a loud "vrooooom" noise. I dont know if its steering related or with the transmission. I check fluid in both and they are full.
3. last issue is when truck is cold in the morning and I put it in reverse there is a deep vibrating noise coming from under the truck but once warm goes away.

If anyone has these problems or solutions or things to check please let me know!

 

Please supply more details, 6 or 4 Cyl., 2 or 4wd, auto or manual. Thnaks