Might just be the busybox wget build
. Kobo's is SSL-less too, FWIW.
Not a massive issue, can be replaced with a custom curl build, or python w/ requests.
The png conversion is also trivial, since you already have all you need (IM) in the screensavers hack.
If you setup stuff properly, rotating the screensaver is also trivial (there's basically nothing to do as long as there's only a single file, c.f., cover mode)
Handling wifi is just a lipc call away (c.f. KOReader). Same for forcing a suspend when you're done.
The actually tricky bit will be to get rtc wakes to behave so you can actually wake the device up and make it do stuff. Here be dragons, because every device does it differently. You might want to take a look at a factory firmware and/or diags, because I seem to remember some helpful rtcwake test scripts in there.