19 month old - tantrums and biting

Hi, I have a 19 month old and am concerned about his behaviour and would love any advice you can give.  He has always been more whiny than other children appear to be (although you only see them for a short while), we don't automatically give him what he is whining about so hoped that would stop.  We are now getting tantrums about everything, these started around 13 months and have increased, more so when he is not 100% well or tired or hungry in the slightest. When I do some research I find things like XX% have 1 per week or 2 per week and so on but this is continuous in the evening mostly but does happen at weekends too .  Doesn't want to get out of the car, doesn't want to go in the house, doesn't want his coat off, doesn't want to get in the chair for his tea, wants to go outside, doesn't want his nappy changed.  You get the idea. When he starts I will go down to his level and tell him to use his words (he has a fantastic vocabulary of around 80-90 words and has a good number of 2 word phrases) and that I won't speak to him until he stops shouting as I don't like it when he shouts and he needs to use his words to tell me what is wrong.  I also tell him I understand he is frustrated about XXX but he needs to calm down and I will speak to him when he is calm.  When I ignore him he really goes off on one but I continue with this until he starts to wind down or if he is flailing on the floor I just ignore him and when he stops we continue doing what we were about to do before the flailing.  I just don't know if this is the right approach, things are not improving and in fact escalating.  I know I need to do something and be consistent so I continue with this but I would appreciate advice.
What has really prompted me to post on here though is he has now started biting.  He did this previously and it was only me (his Mummy) that was bitten and he stopped for a while but this has started again and now his Daddy is getting bitten and yesterday at a play date he looked like he was going to bite his little friend.  He didn't but I am even more worried about this behaviour now.  When he bites me I tell him no, very sternly (and admittedly sometimes loudly when it really hurts), I put him on his naughty stool and tell him he is there because he bit Mummy and it was sore and made Mummy sad.  He then sits there for 1.5 minutes (minute for each year of his life?) and then I go down to him and tell him again why he was put there and tell him to give Mummy a cuddle and say sorry.  He has now started not saying sorry so I put him back on the stool until he is ready to say sorry, which he will do while on the stool but as soon as I ask him to hug me and say sorry he refuses so back on the stool he goes.  This can go on for some time and is completely draining.
He is a very active boy and doesn't sit still.  He is full time at nursery.  I know that he does love me as he gives me lots of cuddles but I find this incredibly upsetting and I just don't know if the approach is right, we want to do our best by him and know he has to have discipline but what is right for the situation is something that we feel like we are clutching at straws here.  It doesn't feel normal for it to happen so much and feels like our nice wee boy is disappearing.  I feel that I must be doing something wrong that it is getting worse rather than better so I really would appreciate help.