Hey Justine - a great start eh? You must have been very please and excited with it!
Skins - when we started I left almost all skins on to make it easier for DS to pick up the fruits as it helps with grip. he either swallowed them or didn't. Sometimes he did and then hacked them back up (whilst I held my breath). These days (3 months on) I don't hold my breath any more, I know he can handle them, he still sometimes swallows one or a bit of one but usually the fruit goes in his mouth with the skin on and a few moments later the skin alone comes back out, or, he keeps hold of the skin and gums and scrapes the fruit off of it then puts the unwanted skin down on his tray and gets another piece of fruit. he pretty much knows it's not the best part to eat. The skins just come out in the poop, I doubt any harm is done.
Small fruits, blueberries, grapes, cherry toms, raisins and things like peas and sweetcorn I avoided for a good while. Even much much older kids can choke on a grape so I cut them in half or quarters now. He's been having all these things for a while now although I'm not exactly sure how long I waited, I based it on my observations of him eating and how I felt he was progressing (really well, like yours he went for it immediately). At the start I was always happier with big things than little things. The temptation to cut things up to bite size doesn't work for me, I felt the bigger then better really so he knows what he is biting off and when it is entering his mouth.
For easier handling of fruit (if you really want to remove skins) you can cut rings with a hole in (ie core the pear then slice into rings) rather than the 'finger' shape. Or try moon or 'V' shaped cuts which are easier to pick up. Softer fruits I eventually discovered if you squish it a bit (just poke your finger into the wedge of melon/nectarine etc) it gives one part where it is 'roughed up' for them to grip. it's the totally smooth cut sides that are so difficult to pick up.
You can also roll in wheat germ or baby rice which gives an initial dry and grippy surface, although I found this went to mush pretty quickly.
Khalams mama, there are very very few things my DS won't eat, but cauli and broccoli are top of the list. I try him every so often but always with other things I know he likes so he won't go hungry! He will put a little in his mouth, maybe even swallow it but he will not pick up a second piece. So it could just be your LO doesn't like those things yet.