Yes, the larger gear size will overstress the chain in the lowest gear and could damage the rear derailer. Insert the new chain in the lowest gear at the back and highest at the front and choose a suitable link to break that will ensure that the rear derailer is not swivelled to far forward.

You need to look at Park Tool web site or another authority to get the correct chain length. Likely yes but you really need to know this process anyway if you're going to be a cyclist. This is the easiest task...

Probably not. It depends on the size of the front (driving) sprockets and the largest sprocket on the cassette.

I have assumed that the smallest tooth count is the same on both clusters.
Provided:
1. your previous chain length was correct for your chain rings/cluster,
2. you have not made any other changes to your setup (chain rings unchanged)...

then you MAY need to increase the chain length by up to 2 links.

Try the new cassette with the old chain and check the chain line from small chain ring to the 27t. If the rear derailleur jockey wheels are pulled well forward "stretched" OR increased derailleur noise in 27t. Then change is probably needed. Otherwise leave chain length as is. Google see below.

Yes, I have one on mine. Cheaper than the 73 and works as well.

Yes it will work fine on the Shimano cassette.

Personally I prefer using SRAM chains because they are easier to install with their powerlinks.

I bought this chain with an Ultegra 9 speed cassette and it works perfectly. I'm fairly certain that the Deore and Ultegra cassettes have the same spacing.