According to JohnR :
Interesting problem. First it sounds as if one of the hot legs is open. Then
you say the lights come on and turning one other devices causes lights or
other devices to be effected. That sounds like neutral problem - or the open
hot somehow reconnected, but in a high resistance state causing the odd
behavior.

All the symptoms are explainable by a loose main feed hot in the panel (or
upstream) making intermittent (and poor) connection. Consistent with
"dropped a leg" terminology.

If the neutral comes loose, 120V circuits on _both_ legs start behaving
"funny", but 240V circuits are unaffected. By "funny", I mean that
some 120V circuits show low voltage (brownout) and some show high
voltage (lights overbright).

The former isn't very pleasant at all, but unless you're unlucky
(as per the intermittent connection), no damage will be done and
it doesn't present a shock hazard.

The latter can be _extremely_ dangerous when 120V devices try
to cope with anywhere up to 240V. Boom. Flames. Etc.

Not only that, under some circumstances, the entire grounding system in
the house can go "hot".

Whenever you see something this drastic happening, it's time to
kill the main breaker and get help ASAP.
--
Chris Lewis, Una confibula non set est
It's not just anyone who gets a Starship Cruiser class named after them.