What's the minimum raise rules of NLHE

Question

assume all scenarios below are 50/100 blind NLHE game

scenarios:

1.The UTG goes all-in for 90, What's the minimum raise for UTG+1?

2.The UTG goes all-in for 120. What's the minimum raise for UTG+1?

3.The UTG goes all-in for 220. What's the minimum raise for UTG+1?

4.If GUT+1 take a legal minimum raise, What's the minimum raise for UTG+2?

----------------update--------------------

5.In scenario 1, UTG+1 raise to 500, UTG+2 all-in 630, UTG+3 call 630, now UTG+1 speak, What's the minimum raise for UTG+1?

6.In scenario 1, UTG+1 raise to 500, UTG+2 all-in 500, UTG+3 call 500, now UTG+1 speak, What's the minimum raise for UTG+1?

....

..It seem there too many situation that let minimum raise change.

Is there one strong rule to solve all these situations?

Answer 1

1. UTG+1 must still min raise to 200 as the blind (100) is still the bet.

2. Again, UTG has not met the min raise so you can still bet to 200.

3. UTG+1 must raise to 340 as the last raise was of 120 (100 to 220)

4. UTG+1 makes a min raise from 100 to 200 (raise size=100), UTG+2 must then at least match the last raise size and make it 300. If there was an all in from UTG as in scenario 3, UTG+1 can min raise to 340 and UTG+2 can min raise to 460.

EDIT:

In answer to your edit, if an all-in does not meet the requirements of a min raise as in scenario 1, you must treat it as if they had called. This is the general rule to solve all such situations.

For example in your scenario 5, UTG+1 has no option to re-raise, he is forced to call or fold. This is because UTG+2 did not raise fully (treat it like a call) and UTG+3 just called (treat it as if he called the original raise). UTG+1 is essentially then facing two calls so, as is normal in such a situation, gets no option to re-raise. In reality he does still have to put in $130 more so he is able to fold if he wishes.

The same is the case for scenario 6 as he has in fact been called by everyone. He gets no option to raise again, or even fold.