Is it true that Army Officers with less than 2 years of active service cannot resign commission?

You can, but it is very difficult to obtain. Usually it will also require the support of your chain of command in addition to a hardship necessitating resignation. Go to Legal Assistance and consult one of the attorneys there for free about your options as this forum really isn't appropriate for them.

You would have to research the reg, but I don't think there is a time requirement. That being said, after the Army invested a lot of money in you, don't get your hopes up on resigning.

I'm likewise not aware of a time limitation other than the Active Duty Service Obligation (ADSO) that accompanies your service contract and commissioning. Resignations at this stage are exceedingly rare but you can always try. It will require the support of your chain of command and placement into the IRR for the duration of your obligation.

Never heard that before. That said, absent some exigent circumstances such a request would be refused on contractual grounds as a matter of course.