Hiya, PL.
Your mum's information is a bit out of date - breastmilk or formula should be the main drink for a baby up to the age of one. Cows milk can be used in cooking, but not as a main drink. It doesn't contain the right balance of nutrients.
However, if you get into a "what you did wasn't right" conversation with your mum, you'll get her back up, so don't, if you can help it.
To answer your questions:
a) No need whatsoever to introduce him to cows milk, especially given your allergy. In fact, that's an ideal reason to cite to people who question your decision. You know about other sources of capcium too.
b) Just water's fine - mine have both drunk just water with occasional sips of other stuff - DS1's just got into smoothies and occasionally orange or apple juice with a meal (he's 3.3), but DS2 still only drinks water (he's 18mo). They both prefer it and I drink a lot of water, through preference, so I don't see it as "cruel" to only give them water, like I know some people do.
c) I work full time and still bf DS2 - he's 18mo. I feed him on demand on the days I am with him (I have three days off and work long shifts the other four days, so I work a full time 40 hour week) and I feed him morning, bedtime and if he wakes in the night on the other days. He doesn't demand that often on days I'm with him and he will go to bed without a feed, or wake up and not have one on occasions when there's not enough time to feed him or I'm out in the evening.
Once you get past a year, IMO there's no need to express, unless you need to for comfort, or unless he's not eating cheese or yoghurt or drinking milk past that age, maybe.
There's a fab page on kellymom here that talks about the benefits past a year, so you can arm yourself with a few facts in the face of criticism.
But do remember that people who criticise you aren't the important people in the breastfeeding relationship you have with your baby. The only two people whose opinions matter are you and your baby. If you start to resent feeding, look at ways to change the relationship you have by altering feeding to only in specific places, at specific times, etc. If your baby weans, so be it, you've done an amazing thing for him and you can be very proud of yourself.
And keep posting here for support if you do encounter lunatics