I made the empty project and set FTP (not FTPs) account. But "Download project" (or Smart Sync) function write "Transferring..." and it all.

Thx.

Did you check the server log?
Did you try to open the target directory in View->Tabs->Explorer to make sure the files are visible and accessible?

Strange behavior, when I use the ethernet connection - FTP work fine, but if connect Wi-Fi, FTP browser conect very long time...
Yesterday, i send crush report, may be it help.

Perhaps, your wifi channel is overloaded with number of connections or the wifi router is too weak to handle them. Try to disconnect all the other tools/software (especially torrents etc) and check after 15-20 minutes.
Anyway, performance of PhpED can't depend on your network transport because it has no relation to the network media at all.

FTP client FlashFXP work fine, without lags. I want to setup Windows firewall or try disable it. If situation will change, i write about it.

still you can explore the server logs to see where the difference comes from.