What actions can an employer take ?

Answer to your question No

1. Is the company entitled to pay for my service during notice period ?

Yes, it is your entitlement and you will get it.

2. If I resign with immediate effect, what actions can the company take against me ? [P.S. I've not signed the offer letter yet.].

In this case the company cannot take any action since you have not accepted the terms and conditions of service offered to you. It is still an offer and no contractual obligation has commenced on your part.

If the company's condition is that you have give one month notice period before resigning during the probation period, you have to oblige the same, since you are in probation period, the company might not have issued you with the offer letter hence the mandatory one month notice period is to be observed.