Learn English – What expression could be used in English to say that you want to discuss to the root of the problem directly

1) To me as a native BrE speaker all of those sentences are OK (apart from correcting "wonder" to "wondering"). Although "check out" originated as AmE it is now heard in BrE too in this context and others. I don't see much difference in the degree of formality. In my experience tradesmen and women are not much interested in formality as distinct from politeness. All the sentences are quite polite with the third being very much so.

If you were going to take a vote, I personally would not use check out, but I would use the third sentence.

2) Other terms: "house call" is associated, but not exclusively, with visits at your home by your doctor. A quick duckduckgo search reveals that there are lots of companies offering PC repairs "at home". Another term often used is "call out": sometimes you are offered service at home with no call out charge, other times you have to pay such a charge. In my experience different traders use their own different terms.

"This is what we have come to" is used in cases where a series of unfortunate or unexpected events have put the subjects (the "we") into a situation that they would not have predicted, and would not have desired.

For example, imagine, in a famine, two people searching through trash for food. One might say to the other "This is what we have come to."

Or, more comically, imagine missing a flight, then unsuccessfully trying to rent a car, and finally ending up in a standing-room-only bus trip for 8 hours. You might turn to your traveling companion and say, "this is what we have come to."

It can, of course, also be used ironically. Imagine the hotel runs out of budget rooms and grants you a 4 bedroom suite. Upon seeing the opulent hotel, you might laughingly turn to your friend and say, "this is what we have come to."