1) How does the running shoe situation work? Is it better to bring the ones I have (white with red), or buy the ones at Lackland?
As long as they are in good condition, and are running shoes you are good.

2)The TSA allows you to bring scissors with blades 3 inches or shorter, but you cannot bring them into the MEPS building. I will have to bring my bag there to get my final physical and swear in before I go to the airport. how do I manage that?
You can buy a sewing kit at BMT.

3)This question pertains to #2. Should I bring a sewing kit with a small scissors? Can I have it at basic and how do I get it there?
See above.

4)It is recommended to get the hard tube of toothpaste, but it is over 4 oz (TSA only allows liquid under 3.4) and is the only hard tube size out there. How do I get that to basic?
Take whatever is travel size and buy the hard tube thing there.

5) What are your suggestions for razors? Should I bring a pack of disposable razors, or a Gillette Pro Glide with some extra heads?
Bring what works best for you that's not a safety or straight razor.

6)On the packing list I received it says to bring luggage or a duffle bag, not a backpack. I was told a backpack was better and easier(plus you need one for tech school). What should I bring?
Bring whatever you want.

7)What kind of compression shorts are available at the BX? Should I bring my own and how black do they have to be, meaning, can they have a grey waist band and a logo? Should I bring my own or buy them there?
The AFI says solid black. Different MTI's will have different rules on exactly what that means when it comes to logos.

8)Finally, is there anything I should not bring that is on the list or is there anything I should bring that isnt on the list?
Depends on what list you have. Some are old and have stupid shit like laundry detergent and an iron which are no goes.