All ball busting aside, I think he's made enough clear signals here that he's in the clear for now. Not to say he may not get friend zoned too if our heroine starts to get a little second-guessy about getting wrong holed by the neighbor. But I'm not sure it'll be because he played "gabby good guy" too much.
At coffee make it clear it's a date. Open the door for her at the very least. Do the ol' hand in the small of her back as she walks past you, through the door. Pulling out a chair is likely excessive for starbucks, but she needs to see #### like that.
IMO if you don't at least get a real hug (not a "thanks for the nickle grandma" side hug) at the end of this, she's going to think you're a #####. You probably don't want to try to suck face in the local dunkin' parking lot... but if a decent kiss isn't something you feel comfortable pulling off, then at least the hug.
The "oo our knees brushed" #### is fine around the kids but you're going on a date, now. Time to man up a bit.