The best place to look for information about public transportation in Paris is the local transport authority.
Metro line 5 takes you from Gare du Nord to Austerlitz. It's the fastest public transport option (unless the line isn't running normally). It's the most convenient (no change, not much walking) as long as you're ok with a few flights or stairs. The stairs will be mostly down because the metro is underground at Gare du Nord and overground at Austerlitz. The metro takes about 15 min, plus the time getting to and from the platform. The metro is well signposted, take line 5, and where you get a choice of direction there'll be a list of stations so pick the direction that includes Gare d'Austerlitz (the final stop is Place d'Italie).
The only case I'd take two metros for this trip is if there's some disruption on line 5. In this case you'd have to improvise or ask for advice based on what's happening.
If you can't handle stairs, take the bus. Line 91 starts from Gare du Nord (so you won't even risk taking it in the wrong direction) and goes past Austerlitz (after going past Gare de Lyon and before reaching its other end at Montparnasse). The stop for line 91 is to the left when you exit the train. In the bus, stops are normally indicated both vocally and on an electronic sign, but in case they aren't working (it happens), Austerlitz is easy to identify: it's the first stop after crossing the river. The bus stops right opposite the street from the station. The bus takes about 30min, plus waiting time and getting from and to the stop, plus traffic (which shouldn't be too bad on this route except for the first few and first last hundred meters).
Either option costs one metro/bus ticket (“ticket t+”). Buy them from a machine (or maybe Gare du Nord still has a manned option, I'm not sure about that). I think you can pay with coins, banknotes (only at major stations and tourist spots) and debit/credit cards. If you're going to be back in Paris, it's cheaper to buy 10 tickets at the same time. They come separately so you can share a batch of 10 and spread them around. They have no set expiration date (I presume that eventually paper tickets will be retired in favor of electronic tickets, but this is still in the distant future).
Both Gare du Nord and Austerlitz have plenty of eating options. If you aren't going to eat on the way or in a restaurant, the Austerlitz area has much nicer spots: the Jardin des plantes has benches under trees (no promises about them not being occupied), or you can take a short walk along the Seine.
While the pandemic protection measures are ongoing, masks are mandatory inside all public transport, including buses, trains, and stations. As a consequence, eating and drinking is forbidden.