Before becoming a governor I used to help regularly in my child's school - the usual tasks like helping little ones change for PE, mending books, washing paintpots etc. I saw no reason not to continue when I was elected a governor (do you?) but sometimes feel awkward not knowing which role I'm in. Teachers may bend my ear about small grievances or point out things that need money, or the head may walk in and talk to me about something that's coming up before governors. I don't know how far to get involved. Also I may hear remarks which could be harmless or could be a bit snide, like "Now that you're so important ... hope you won't think this too trivial."
Such remarks usually mean the speaker is uneasy about you in some quite fundamental way and is playing it both ways. Teachers, and indeed heads, find it hard to get used to parents having a serious role and show their uneasiness by this form of nervous half-joke.
You raise several points. First, no, of course there is no need to give up your classroom tasks: I always think it helps one's credibility as a governor to be involved in useful and uncontroversial things. Second, teachers bending your ear. You must pleasantly discourage this: if it's a matter proper to governors, teachers have their representatives to see that it gets on the agenda. If it's not a matter for governors they have their own internal committees, their unions and ultimately a grievance procedure to seek redress. Besides, if a gripe became a formal grievance you might be involved formally, hence it would be improper to have discussed it informally.
In the same way I think you should side-step discussion of actual governors' business with the head, because although it may be innocent it could put you in a difficult position (as you realise) by making you feel you've been "nobbled" or compromised in some way. If a head is apprehensive about how a particular issue will go down with governors, the temptation to sound out or even pick off a friendly soul who happens to be on the premises could be hard to resist. There is no need to be heavy: just say you look forward to discussing that at the personnel committee, for example, or you will be interested to hear what other governors think.
We all have problems of role boundaries to some degree: parent governors are perhaps especially exposed. I think I am saying that you stay with the role you are in at the time. If you are washing paint brushes, you resist getting drawn into discussion of the arts in the curriculum, but keep it light. If you are at a governors' personnel committee, you try to forget that teacher who was sounding off about never getting promotion when you were helping in school, and you'll be grateful you didn't encourage him or her.
You said you need a bigger quorum for co-opting a colleague than for setting the budget. I am amazed. What is your logic?
The normal quorum applies to most governors' business. The exceptions are cases where the governing body is empowering people, either fundamentally and permanently by making them governors, or partially and temporarily by delegating a function to a committee. That, as I understand it, constitutes the logic.