Yeiks!! That dryer tube is definitely a disaster waiting to happen. There's absolutely no way it should be kinked up behind the machine like that.
We've a Miele vented dryer, and I give it and its metal vent ducts a good vacuuming once in a while.
It's very easy to just slip the nozzle off the vacuum cleaner, turn it up to full power and slide it through the ducts. You can also use a small chimney brush to clean out the ducts if they're very long.
After that, I vacuum the area around the door filter, any ducts I can get access to etc etc.
Also, he didn't seem very concerned about the rest of the duct i.e whatever that little bit of dryer tubing was connected to ... if that's blocked up with lint or or kinked / damaged it's an equally big problem.
As for cleaning the washing machine with just detergent and bleach. Yeah, that will kinda work if you've got no "gunk" in there to start with
I'd suggest this, particularly if you never do hot washes:
1) Descale the machine using an approved washing machine descaling product.
2) Run the machine with a disinfectant solution on a hot wash e.g. laundry sanitizer or something that is approved for that purpose in a washing machine e.g. some of the liquid disinfectants are.
3) Leave that solution in the machine over night to kill all the bugs.
4) Complete the cycle.
Descaling once in a while is very important if you're in a hard-water area, and particularly if you have a front-loader which has an internal element.
If you do hot washes regularly, and your machine looks and smells clean. You can give that a skip completely!
You should, however, wipe down any seals with a damp cloth and if it's a front loader, check the pre-pump coin-trap / filter for any debris i.e. coins, buttons or other items that may have found their way in there during the washes etc
Typically, this should only need to be done about once very 6 months (or, if you know that something has gone into the machine or it is draining slowly. The filter is usually self-cleaning and the pump will pass any lint, or even small buttons without issue.
You should also rinse out the detergent dispenser / fabric softener dispenser on your machine front or top loading (if it has one) with warm (not boiling) water to dissolve any fabric softener or detergent that has lodged there.
Front loaders drawer dispensers should be wiped out with a warm damp cloth with some mild disinfectant too.