It helps if you try to separate actual bad behaviour from behaviour that you feel is trying.
"she is arguementative and seems to enjoy it. sometimes she makes a statement and when we agree she argues the opposite point"
Try to relax and enjoy it, store up some of her most bizarre arguments to tell at her wedding dinner. It does not mean that she will turn into the teenager from hell. Besides, quite frankly- the world needs people who question things. My dd was exactly the same and (once she had learnt to keep it within socially acceptable bounds) grew into a very interesting person to talk to.
"when asked to come over or stop doing something she never cooperates, she always says no or in a minute or im busy colouring etc."
Yup, you can never ask a 2yo to do something directly, they need to be given warning ("We're going in 5 minutes' time; when you've finished that picture; after I count to 50"). They may need further help to tear themselves away- like waving bye bye to the swings.
"at the dinner tabel she fidgets constantly, getting up and down, kneeling up sitting down, pushing me or dp with her feet, banging her spoon, talking/singing loudly, saying yuk to things. dp has now put her back in a highchair till she sits properly but this has backfired as she says she likes it."
Try to sort these into behaviours that you want to change immediately, behaviours that you want to change over time and behaviours that don't really matter, at least for the time being. I would clamp down on pushing, correct her gently when she says "yuk" and ignore the singing (for the time being, doesn't mean you won't deal with it later). And if she likes sitting in the highchair, let her.
"every time we leave the park she has a massive tantrum, says no, runs off and has to be carried out kicking and screaming despite being given a 10 min/5min warning."
That you may just have to live with. It won't last forever. Am not now carrying a screaming 13yo.
"she has to be reminded of please/thankyou most of the time."
Yes, and that is your job, to do gentle prodding without losing your temper and making her feel there is something unpleasant about pleases and thank yous.
"when strangers speak to her she ignores them, even people she knows like neighbours so she appears sullen."
Normal and quite likely due to shyness. I was exactly like that and I have not grown up into an antisocial loner. If you give her time to come round instead of pressing her, it will pass all the quicker. In the meantime, just keep modelling how much you enjoy talking to different people, let her see that it is fun and not scary.
"she shouts in public, no i wont, leave me alone, stop dragging me (when being removed from park) and people stare because she sounds so rude."
I feel your pain. But it will pass.
"her behaviour is embarassing and its getting to the point of us not wanting to take her for meals etc."
I do get the feeling that you worry a lot about being embarrassed by her. Try not to- most people have seen 2yos before; they won't be judging you. Very few of us are able to impress other people with out beautifully behaved toddlers; it's one of those dreams that you have to let go of.