Hi and welcome to YT! Congrats on getting Layla.
Yeah, you might want the vet to check the drooling and the tearing eye - it could be allergies. However, at 5 months old, she is also teething - getting ready to get her adult teeth so it might be related to this.
With the eyes, other than allergies, it could be as simple as making sure no hair is poking her in the eye. Mandie's eyes used to water a lot more than they do now. I changed her food to grain free and started giving her filtered water (some even give the Gerber baby water or distilled water). There is something about the hard water in some taps that could cause the tearing.
Tricks, you can start those at any time. We have a member who has a 21 week old puppy who has been doing tricks for weeks already. Very special, but shows it is never too early. Just schedule time with Layla and you alone (with little treats of course) each day and work on some basics like sit, stay, come and build on that.
OH, also..post pics of both Layla and Morpheus when you get a chance. We LOVVVVE us some pics around here