The speech delay is unfortunate for her, but then it is good that she can say the longer sentences you mention. In the last few days I have replied to several parents with 2 to 4 year old children, who are very shy and quiet at playgroup/nursery, and people speculate about children being 'selectively mute', but I think it is because of the less familiar environment where they don't feel entirely 'safe' to be themselves.
Don't worry too much about the counting and word recognition for now, nor about not concentrating on TV, which should be kept to a minimum anyway.
That is interesting that she is so 'physical', and I think to concentrate on and develop these skills. So help her to improve at the things she likes; maybe when she is on the trampoline, help her to count the number of jumps she can do.
You say she collects objects in a bag; what sort of objects, and is there any link or pattern to things she likes to collect?
If you can, build up the longer, more complicated sentences and discussions with her, perhaps even keeping a written note for information, to monitor how much she can do, and how it develops.
Duplo is good, as it can be used for counting, learning colours, matching shapes, as well as the more obvious 'building up and knocking down'. Do you have any child-safe scissors? Cutting up junk mail, catalogues etc, and maybe sticking in a 'scrap book', or sticking on thin card to make your own jigsaw puzzles. Threading-laces, and large beads (too big to swallow) or cotton reels are good for manual skills.
Does she help you cooking; just playing with pasta, flour, ice-cubes etc can be stimulating.
I'll look back sometime to see how you get on.