What’s wrong with buying the one month ones? I will get the money back sooner and can then redecide what to do with it.

Nothing "wrong" with it. It's just important to be informed what exactly it means. For example, on 11/19/24, you could have bought a 4-week T-bill with a yield of 4.609%, or you could have bought a 13-week T-bill on 11/21/24 with a yield of 4.526%. But had you bought the 13-week one, you would have received 4.526% for the entire ~3 month period. The 4-week T-bill would have to be reinvested a few times. You would have bought another 4-week T-bill on 12/24/24 at a yield of 4.334%, and then again on 1/21/25 at a yield of 4.339%. You can see that when rates drop, it is sometimes better to lock in a slightly lower yield for a longer period rather than take an initial higher yield, but then have lower yields upon reinvestment.

Is there any friction cost (fees, spread) buying tbills on IBKR?

Usually when you buy "new issues" (i.e. buy directly from the treasury via you broker), there are no fees, so your yield is exactly the yield that results at the auction. But when you buy T-bills that are traded on the open market, there are spreads and sometimes fees.

there are strips and many not very clearly understandable names. Which one you guys buy?

In general, if you want a treasury instrument, they are pretty much all equally rated (equally safe), so you pick your maturity date, and you buy the one closest to that maturity date that has the highest yield AFTER fees and spreads. Lately I almost always buy new issues with no fees or spreads.

Say I bought a 1 year bill, and then I decided I need the money (to buy stocks). Do u sell it or get into margin debt?

Yes. You can choose either one, sell it, or use it for margin. The margin on US Treasury securities is VERY high. In my experience, it is rarely worth actually going into margin debt for these kinds of things because the margin interest rates are substantially higher than what you are earning on the treasury debt.