here are the ICs i bought (are these fake?)
Read this post and compare date codes
Counterfeit MCZ3001DB chips are being made in China and one person on another forum said his TV caught fire after installing a fake. It's probable some of the fakes are good but others may be decoys and others may be dangerous. Many of the capacitors and other electronic components sold on eBay are fakes.
Sony doesn't make them, the originals were made in Japan by Shindengen. I think Sony did supply them to authorised repair places at a higher price. It should still be possible to order genuine MCZ3001DB chips through Amazon (from "B&D") and a few other reputable parts websites such as the ones listed on this page.
The Pacific Semiconductors mentioned on that page lists plenty of stock. Audio Labs of Georgia lists their MCZ3001DB chips as "Tested.".
the shop said they have the ICs in stock so might just go with theirs and return mine.
they were supplied by Sony they should be fine but I'd doubt random eBay ICs. You should inform them there are fake MCZ3001DB chips about though and that some of the real ones might be dead on arrival.
should i make sure they use sockets?
Yes. Usually for this kind of IC repair a socket wouldn't be used. But these chips can fail again and having a socket makes it much easier to deal with a bad chip.
should i also make sure they dont solder the pins holes that werent soldered in the first place? i believe its pin #13
Yes but if they know what they're doing they're unlikely to do that.
will a error code need to be cleared after the repair?
No, it should turn on normally although it's possible the TV's picture might have changed slightly because of voltage improvements.
do you know how i should clean the CRT tv's screen?
I don't but I know many cleaners can damage or cause streaks on a TV screen. A clean microfibre cloth is a good start. The screen scratches and retains fingerprints really easily so that's something to be careful of.
The two MCZ3001 ICs on the D board don't fail in the same way as each other so it's usually possible to revive the TV just by swapping the two chips. But it's preferable and probably safer to have the professional install two new chips.
Your model, the 34xbr800, should have DVI with HDCP which is effectively HDMI without digital audio. It should be possible to plug an HDMI device into it with an HDMI to DVI adapter and a couple of RCA cables for the audio.