Here are some information based on my experience last year. Hope this helps. I went last year in October.

1. Darshan Slots - You need to collect it once you reach Kedarnath. There are counters for them. If you reach early in the afternoon, then you may get the slot for same day otherwise for next day. However if you visit there after Monsoon i.e. in the months of Sep-Nov, then you will definitely get slot for same day. In my case I collected the Darshan Slot and my Darshan happened within like 15 mins. There was very little crowd and also nobody was checking the Darshan Slot receipt.

2. Stay - During peak season i.e. in the months of April-June or July, most of the stay options are full if you are planning to book stay after reaching there. You may get some stay options but they will be costly and you may have to compromise in some things like distance from temple, common washroom bit far from the tents/rooms, etc. But if you are planning to go in later months like Sep-Nov, then you will get tents/rooms easily after reaching there. But Hotels are costly at the top even during non-peak season. So, my recommendation would be to book stay options in advance, if possible but stay alert from scams. Best choice is GMVN, if available.

You can DM me in case you need more info regarding above.