I know that while applying for visa my passport has to have at least 6 months of validity. 

 

1) For how long the passport has to be valid prior to entry though? 

2) And for how long passport has to be valid for visa exempt 30-day entry? (Land border from Laos) 

1. Most passport holders from countries that qualify for a visa exempt entry only need a passport valid for the length of stay to enter Thailand. Others need 6 months of passport validity.

2. You would need 6 months of passport validity to enter Laos. Same as number 1 to enter Thailand.

My suggestion though is never allow your passport to go below 6 months of validity.

As @ubonjoe says, relying on a passport with less than 6 months validity is asking for trouble (albeit, many countries' nationals are allowed to use such passports to visit Thailand). In most cases, if you have a sudden unexpected need to travel, you will be scrambling to get an emergency travel document, as only a handful of countries will allow you to enter with a soon to expire passport.