Just like sausage domestic animal fat (pork or beef) is for the finished product. In some case it does add taste yes but most don't do it to cover up the vension flavor but rather to have it moist and stuck together. Personally I don't add any fat to my venison grind at time of process as there are receipes/uses where fat isn't required (such as chili, taco's, meat sauces, etc). When a dish does require some fatt content ( burgers, sheppards pie, etc) then I add fat at time of preperation. Venison if packaged properly (void of air) will last 2 years in a chest freezer, domestic pork will last 6 mos & beef 1 (max)...reason being fat content! Just a Cliff Claven Factoid for you!
In regards grinding I double grind all the time. I start with the larger plates and go down a size(I use a 9/16" and 7/16" equiv. diameter plate for burger). For sausage I use a 9/16" for the intial grind, then a 1/2" for the secondary grind after the spices and meat mixing stages. Also when making sausage I let the mixture sit for 3 hours refrigerated prior to re-grinding and stuffing. Just like merinating it allows the spicing to sink into the meat and disperse (reduces pockets of over/under flavouring).
The gristle can come from under grinding or under trimming. Cuts such as the shank and front shoulders need more attention. Try seperating by muscle group, if you find working with larger pieces of meat difficult simply hack them down to your comfortable or workable size. Always will be a grind pile and small piece grind up as well.