OK, on the MBAM log.
See if you can find this file h@tkeysh@@k.dll in the system32 folder, if you can, manually copy it to the avast chest, I want you to send it to avast (see #### below for instructions), before running MBAM again as you didn't select any action and we want to remove the stuff found. See below ~~~~
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Add the file to the User Files (File, Add) section of the avast chest where it can do no harm (see image1) and send it from there. A copy of the file/s will remain in the original location, so you will need to take further action and can remove using MBAM.
Send it from the User Files section of the chest (select the file, right click, email to Alwil Software). It will be uploaded (not actually emailed) to avast when the next avast auto (or manual) update is done.
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Run MBAM again in normal mode first as you started that way.
Run MBAM and this time when the scan is complete,all detections should have a check mark in the box to the left of the entry, leave them selected (or select if not selected). At the bottom of the window there is a button, Remove Selected, click that and the items will be removed, see image2.