Yes, the Navigo Decouverte will work well if you are arriving on a Monday and leaving on a Monday so you'll have all 7 days worth of transit.
You don't need to upload photo but you need to bring one with you. I just photocopied my passport photo page and then trimmed down the picture to meet the guidelines. IF you forget, your hotel can photocopy your passport page for you and likely will lend you scissors, lol. Just bring the pictures (do not have to be on good paper or photo paper) maybe in a small ziplock bag and you can use them when you assemble the pass. I go to a Metro Station with a manned window OR to a Tabac near my hotel to do this transaction. I do not know if Varenne has a manned window as that's not my usual station, lol.
There are many restaurants within walking distance of the Varenne Metro.
Do you have an interest in WWII? There is a cafe on the other side of Les Invalides on Avenue de la Motte-Picquet that has a connection to the French Resistance. I've not eaten there as I'm vegan and the menu looks pretty "meaty", lol but it sounds so cool!! It's Cafe Max and it's location between Les Invalides and Ecole Militaire (the military school where Napoleon went) where German officers were stationed made it perfect for snooping.