Let's go through each issue raised in your post.
What is the procedure for foreclosure after bankruptcy discharge is final? The lender has to go through the ordinary foreclosure procedures under your state's laws. Since your bankruptcy case has been closed (which is what I think you're trying to say), the lender doesn't have to deal with bankruptcy procedures.
What does "deemed abandoned" mean? Apparently, your Chapter 7 Trustee did not care to try to sell your house, and now your case is closed. So your house is no longer the property of the bankruptcy estate. [Your house WAS property of the bankruptcy estate while your case was open and active.] What your lender might be trying to say is that the house has been 'abandoned' by the Chapter 7 Trustee.
Do they have to go through the foreclosure procedure again? No. That's because simply waiting for time to pass is not an "action" that's prohibited by the automatic stay. So if you were already served with foreclosure notices before you filed BK, then time passed while you were in BK. Now the BK is over, and the lender can continue with the foreclosure process.
Regarding the required notices and the foreclosure procedures of your state, you will need to see local counsel.
The broad answer to your question is yes the foreclosure process will need to be completed. During the pendency of your bankruptcy case, your estate became the trustee's estate. The trustee has abandoned his/her interest in your real estate, meaning the trustee sees no value in the property. Therefore the lender can now continue with the foreclosure.
Regarding the timeline, that is anyone's guess. The foreclosure process can be somewhat lengthy in Ohio. The typical process is Complaint, Judgement, Appraisal, Order to the Sheriff to Advertise and Schedule the Auction, Advertisement, the Auction, Certification of the Sale, Request for the Deed, and then a Writ of Possession.
You will continue to receive notices regarding the foreclosure case because you are still a necessary party. What you need to do is read the information sent to you so you know at what point of the process you are in. You should also contact the Sheriff's office to keep up to date on the sale process once the property is schedule for auction.
If you have not made other living arrangements, you should probably begin. Again, the amount of time you have until you are asked to vacate can very quite a bit, there really is no set time because any number of things can delay the process. I wish there was a set timeframe but unfortunately there is not.
If you do vacate the property before a new deed is issued transferring title to someone else, you need to make sure the property is maintained and the grass is mowed. Until title passes to someone else you are still the owner of the property and you do not want any Health Department Violations brought against you.
The Chapter 7 bankruptcy discharged your obligation to pay the mortgage if you did not reaffirm the mortgage. However, it did not remove the lien. If you stop paying on the mortgage and do not catch it up, then the mortgage company can begin foreclosure proceedings following state law. If the mortgage company started foreclosure proceedings before you filed for bankruptcy, your filing stopped them. They need to start over now.
[This communication is intended as general information and not specific legal advice, and this communication does not create an attorney-client relationship.]