The 4000 has its issues but over all is a great machine. Make sure that you take the cover off first thing and look at the battery. If its still the old barrel type remove it immediately and hopefully it has not already leaked.
depends on further cisrcumstances. if its board rev. B (most likely) it will have a barrel battery, then either it has been replaced by the previous owner or not. most important is to look at corrosion traces around it and remove it immediately if there are any. if its rev D it will have a coin type one, that isnt likely to leak as previous but likely needs to be raplaced or removed first.
The Indivision AGA from Amigakit is your best option for video then you can use any LCD on the market.
im not sure a version of indvision compatible with the a4000 si easily available, and would first try to confirm the amiga working reliably before further considerable investments. so id use some simple scan converter first. unfortunately i have displays at hand that do not require any further devices to display amiga signal, so i cant help with it.
