Again, thank you very much for your reply! 🙂

I just turned the Wallet back ON and checked how it works now. So, here is my report how does it look like on my side.
It seems like it works much better than before and picking more or less the whole data, (I hate to say this) BUT...

Let me explain what I think might be the problem...
When I refresh the Wallet/Transfers page (with SteemPlus Wallet function ON) first few seconds I can see the whole data there, including the last transactions of few minutes or even a few seconds ago.
But when the page fully loads, and when those boxes, in the space between the sentence "Beware of spam and phishing links in transfer memos..." and the first row in the list of the transactions appear (I'm talking about "Add private memo key," "Filter by type," "Search," and "Min Amounts" boxes) - it seems like they are covering first or even maybe first few lines (rows) from Transaction History List.

Maybe it's just some sort of page formatting issue, where is needed to leave more space for those boxes to avoid overlapping with those first few rows from Transaction's History. I'm just guessing! I don't know, but I think somewhere here might be the solution.

However, that's how it is on my side at the moment! 🙂