As you haven’t given the itinerary it is only possible to give general advice.

Practically all trains in Germany (and Switzerland) are valid with your pass.

Make sure your app is up to date, use google play/apple app store.

Search for the trains individually, different planners give different results but the individual trains should be there and you can always add them separately.

In Germany trains listed as IC, ICE, EC can be reserved, R, RB, RE cannot be reserved.

The best place for reservations is www.bahn.com or the DB planner app, they also show a seat map so you can pick available seats beside your friends.

I was able to finally find it but it is saying eurail pass isn’t valid for the last part of the trip from Dortmund (the tram in basel is not included?) and I can’t book a reservation for ICE from Dortmund to Basel at all, even though it says it is included in the pass. my friend bought on trainline and it shows the trip going all the way to basel sbb arriving at 22:55 (and no mention of a tram, just the ICE) so not sure why this one is showing differently on eurail app? here’s what’s showing on eurail:

16:36

DORTMUND HBF (Germany)

6h 6m

ICE 5203

ICE

Direction

Basel Bad Bf (Switzerland)

You're ready to board

You can buy a seat reservation if you like but it's not required.

Prices unavailable

No price results were found. Pass holder reservations may be sold out for this connection, but there are other ways to check for available seats—more info below our timetable.

More information

22:42

BASEL BAD BF (Germany)

0h 7mTransfer by footShort transfer

Need more time?Adjust your transfer time in filters

22:52

BASEL, BADISCHER BAHNHOF (Switzerland)

0h 10m

TRA 2244

Tram

Direction

BINNINGEN, KRONENPLATZ (Switzerland)

Pass not valid

Choose a different journey within the Pass network or buy a separate ticket for this journey.

23:02

BASEL, BAHNHOF SBB (Switzerland)

Either Eurail or Trainline could not be up to date. Some ICEs terminate at Basel Bad Bf in the evening. I'll have a look.

EDIT: that ICE should continue to Basel SBB unless it is heavily delayed (frequently happens lol). Log the journey later, on the day. If Rail Planner is still not correct by then, add the last bit manually.

Please next time avoid third parties: no benefits, you'll only get problems.

No, the Eurail Pass is not valid on trams, buses or subways. A ticket is around 3 CHF or you can walk depending on where your accommodation is.

The Eurail website is the worst place to book seats: they're more expensive, they add 2€ fee per person per train, no seat map, sometimes only paper reservations, etc.

As suggested use the DB website/app for reservations. 5.20€ with seat map.

However it doesn't work at the moment through DB. I guess there are some uncertainties on the train type. Check back in a few days.

So there is no way to guarantee I have a seat on these trains, is that correct? Since the deustche bahn website won’t allow a seat reservation either? I just have to wait until that day and hope there is space to ride along with my friend?

Also we selected first class. Is first class usually full on these types of trains?

You can reserve seats on that train via www.bahn.com

Make your search in the search window, and select book seat only when you filled out your destinations and preferred time and class. I see still seats left in 1st and 2nd class. 

What is not reservable is the city tram from Basel Bad to Basel SBB. (But your train should continue to Basel SBB). Look where your accommodation is, and choose the closest station for convenience. 

Does it work for you @BrendanDB ? I get these error messages for the ICE:

I'd try again tomorrow or in a few days. German long-distance are always busy (especially from/to the Ruhr area). Make a reservation (when possible).

I cannot get the reservation to work. getting error message like above from Dortmund to Basel:

Reservation cannot be made

Yet you can buy a full ticket on Deustche Bahn for this exact journey. So why can’t I reserve a seat? I would be sad if I can’t travel on the same train as my friend for a 6+ hour ride lol

Checked again, and now I indeed don't manage to get a reservation for that specific train any more @thibcabe  @s8833@s8833. The train later and earlier don't give problems, weird

There seems to be some differences of opinion as to where this train is actually terminating.

DB has it as Basel SBB,

OBB tickets has it as Freiburg

OBB Scotty has it as Karlsruhe.

Seat reservations are available on DB to Karlsruhe but no further while they will sell tickets to Basel.

OP you could get reservations from DB from Minden to Karlsruhe on the same trains as your friend.

If ICE5203 does run through to Basel then you can just stay on, the train will likely be emptying out by Karlsruhe anyway so you won’t have a problem with seats, just make sure your pass is correctly set to Basel.

If the train does terminate at Karlsruhe or Freiburg then you will both have to change to the next available train anyway.

Also, German trains are not reservation compulsory, even without reservations you can still hop on board and take any available seats, ICE5203 is listed as “low demand expected” by DB so it should have plenty of available seats.

Interesting! I didn't look from the other direction…

This message could include ICE5203 then:

There will be later trains. Only expect to arrive later than planned in Basel (usual in Germany anyway).