Hi redfox welcome and welcome Borttagen
redfox, My dd (2.6) has a zebra and I can honestly say it is the best thing we have bought. It has given her her independence to explore and even cause some mischeif!! She whizzes around, can go though cupboards and into differnt rooms, explore the garden without relying on me to be at her side constantly. When we first got it 6 months ago, she could sit on it but was very wobbly and had a few tumbles but she soon with practice worked out how to scoot first with pushing both legs together and now moreoften but not all the time alternately which is brilliant and her stability has improved a million percent. I can't recommend it enough! It makes me so so happy to see her being independent 
In terms of transitioning herself onto it, she mainly relies on us but is now working out with a little support on her core where to place her hands and how to pull herself on by herself.
You will see from some if my posts I am a bit worried about my DD speech, but from what you say, your dd seems very much on track for her age, even so I appreciate that wont stop you worrying!
We have been told that understanding is far more important than actual words, so the fact she understands commands is very positive. you sound like you are doing all the right things, We have been told to keep reading, siniging, repeating sounds back and also allowing silences and time for dd to respond without jumping in.
Bortaggen. DD didnt hit any gross motor skills for ages! Rolled at 14months, and sat at around 15-16months and it has only been the last few months that we have been confident to take the cussions away. sneezecake on here recommended the best book and now I tell everyone about it its called 'teaching motor skills to children with cerebral palsy and similar movement disorders' by s.Martin. I am constantly referring to it For tips and advise on exercises to encourage motor development, Are you seeing physio ?
The early days are really tough particularly the unknown, but on this board you have people who really understand and it has saved me. I hope Monday goes well.