Sorry if I couldn't respond sooner; I was logged out for a while.
Anyways...
1) Yes you can. The only book by another author that truly takes place after a Salvatore book (to my current knowledge) is the first book in Elaine Cunningham's 'Starlight & Shadows' Trilogy. It takes place after events in the third Paths of Darkness book, 'Siege of Darkness'. After you read that book, many of the mentionings in from the 'Starlight & Shadows' books will make MUCH sense. However, I'd only suggest reading this series if a female drow protagonist (who is a bit like Drizzt in how much both are exceptions of Drow culture) interests you, and/or you're looking from a temporary break from continuing through the Drizzt books up to that point.
2) If you're looking to see the chronological order of Drizzt Do'Urden's life to the latest book, then this is the pattern you should take. Start with the 'Dark Elf Trilogy' first, since those explain Drizzt Do'Urden's origins. Next, read the 'Icewind Dale Trilogy', as that pretty much continues things from there. After the ID trilogy comes the 'Legacy of the Drow' series. After LotD comes the 'Paths of Darkness' series. Finally, after PoD comes the latest series, the 'Hunter's Blades' Trilogy, which are the latest books. These books, in that very order and from book 1 to the final book in each series respectively, chronologically follows the path of Drizzt Do'Urden and his companions.
Does this make sense?