Is it possible for two nodes to view blockchains differently? Is there a chance, that at some point in time, two blocks will have different number of confirmations, according to different nodes? Like, with difference up to 3-4 confirmations?

The problem I'm having that I have Iquidus Explorer set up as my SolarCoin blockchain viewer and I have 6 as min. number of confirmations until it gets picked up and written in a database, but sometimes, transactions are written there before they show 6 or more confirms here.

Thanks in advance!
Absolutely! This is why consensus is so important in Bitcoin. If there is a fork in the chain, a transaction could have 1 confirmation on one fork, and 3 on the other fork. Eventually one of these forks is going to win out and become the defacto blockchain. I don't think 3-4 confirmations would be common in Bitcoin, but if you are on an altcoin it definitely seems feasible. Testnet3, bitcoin's test network, routinely has these competing chains for short amounts of time -- after there is a clear winner the losing chain reorganizes on to the longest chain.