Veteran Germany travellers; we have always rented a car (except in Berlin)- but with the price of gas and the ever-worse traffic congestion, am contemplating riding the train this time---does an itinerary of Frankfurt-Nuernberg-Erfurt-Leipzig (perhaps)-Berlin-Cologne make sense? Rest of the holiday is in countryside, so would rent car for that. Would railpass be the best bet? Does DB give other discounts to seniors?? Any info will be appreciated----

Railpass could be the best option - depending on whether you need flexibility or not to just hop any ole train anytime

www.bahn.de the German rail web portal has all the regular prices along with any online discounts that may be available - if you go this route you must reserve as early as possible to secure these limited availability fares and they are non-refundable non-changeable i believe.

And there are regional passes (Lander i believe they are called for use of regional trains and local transport but not fastest trains like the crack ICE trains that go up to nearly 200 mph on some routes.

For full fare you have some long costly trains and the railpass would be a good deal i believe if you want flexibility to go to the station and just hop on the usualy at least hourly trains between cities.
For pass info i always advise some sources that give you much more than just the price of passes and an option to buy button: www.ricksteves.com and www.budgeteuropetravel.com - they each have lots on train travel in Germany, the K-D Rine Boats (100% covered by railpasses), passes with current prices, etc. Pass prices are universal no matter where they are bought but shipping fees can be added - many agents have no fee but some may have $15-20 handling or mailing fees.
As for senior discounts on www.bahn.de put in your age to get the price quote reflecting senior discounts, if any (60 and over)s

There is i believe a Senior Card you buy for the year but costs about $80 or so so not viable for a few trips really vs the pass (not sure on Senior Card price, etc. but again see bahn.de

Yes, all your destinations have good train connection. Some of these connections (Berlin-Cologne) will be much faster by train than by car.

For tickets and prices see www.bahn.de

Full fare flexible tickets for the OP trains: (from bahn.de)

Frankfr-Nurenberg 46 euros ICE

Nurnberg-Erfurt 47-68 euros depending on the ICE you take
or 35.5 euros on regional train (takes an hour more)

Erfurt-Leipzig 27 euros

Leipzig-Berlin 40 euros

Berlin-Cologne 102 euros

Note 29 euro online discounts are possible on all the above if you secure them far enough in advance - non-changeable non-refundable fares.

But for flexible fares where you can go to the station and hop on any train (no reservations required, optional) total would be
262 euros p.p. (adult) or $420

Discounted route: 143 euros or $230 p.p.

COMPARE WITH RAILPASS
5-day German Twin Pass - five unlimited travel days of your chosing in a one month period (two names on one pass, cheaper than two individual passes) costs $238 p.p.

Just $8 more than going the advance discounted online route so for $8 more you can get fully flexible trains with the pass

If i have added right it would be a non-brainer to buy the pass - of course that's if you do go to Berlin of course.

There is also a German Rail/Drive Pass that mixes a number of days of rail travel with an Avis or Hertz car rental

take the train a long distance to a station and then drive a few days thru the Mosel Valley or some other neat rural area not served well by trains, then return it at another station to hop on a bullet train and blast elsewhere

not having to drive long distance will save lots of gas money and car rental prices per day and let you to ditch the car upon arrival in a large city, where more and more cars are either banned or parking is impossible, etc.