Just went through the same thing, you will indeed by seated in economy on LH.

As mentioned above, the only difference between biz and eco on LH intra-europe flights is the blocked middle seat, so, I would say it is definitely not worth using miles or anything else to upgrade.

With regards to seat selection, I was able to select exit rows without an additional fee on my outbound but not my return. I assumed this was something to do with connecting J->Y on the outbound, but, starting off at an LH station in Y on the return.

I have a Senator card so I cant comment on baggage allowance or lounge access on the return, but, I would assume they would let you in as you have a same day connecting flight in business.