I have 2 Oyster Cards from previous business trips (one is 10+ year old and the other is 15 months old).
2. We'll be going just around touristy parts of London for about 4 days. What type of tube/train passes should be we buy? Is it worthwhile to get a Railcard (I believe for 30 GBP) just for 4 days? I read there is an unlimited daily pass that can be restricted to specific zones too.
A railcard is a discount card for train travel. As you are only travelling in tourist London you are unlikely to use trains and even if you did, inside London you can just pay by Oyster or contactless device anyway. Although a railcard discount can be applied to Oyster cards, you are not going to spend anywhere near enough to make back the £30.
Not sure if 10 years and 15 months refers to your children or your Oysters. Inside London children under 11 are always free when they travel with you.
If you have a very old Oyster (without a D in a square on the back) it may need to be replaced before you can use it again, however new Oysters now cost £7 whereas you can use a contactless device to travel at generally the same prices as Oyster. Using Oyster or contactless will always cost the same or less than a daily pass (for your purposes), because once your travel in one day has reached the price of the daily cap you will not be charged for any further travel.