2. You can use either the direct or indirect relative with "cá huair".
7. Yes, if you're assuming it's a female you would use "cé hí" (and "cé hiad" if it's more than one person), remember to change "air" to "uirthi" too.
There's no real consensus on the correct citation form these days. You could say "cuir ar", "rud a chur ar", "cuir ort", "rud a chur ort". It used to be that the 1st person singular was always used as the citation form of verbs, so in older dictionaries you'll see "cuirim (rud) orm" for "to put (something) on".