Welcome back! Exciting times ahead for the A500 with the new Vampire which will solve a lot of your needs in one go. Bit of a wait for that though. In the meantime, you need to look into writing ADF disk images onto a floppy. I am guessing that some kind of serial link up to a PC may be the best bet as it would be easier than trying to find a catweasel or other flexible floppy drive platform.
LCD output would be by the way on the Indivision. Amigakit has them. I got one for my A2000 and it's a must buy. The only other option is to find an LCD screen that will sync down to 15khz.
Not aware of any ethernet solutions for the A500. I am guess you could get a Lantronix UDS-10 and connect that to the serial port. I defer to others here with greater knowledge.