The answer to your first question, is not necessarily. Some universal players, mostly Oppo, have multichannel analog outputs that can be used with SACD, but generally your are limited to universal players, not boutique hi end SACD players which are just 2 channel. In that regard, the only game in town is the Sony X800m2 or Sony X1100es unless you pay out the nose for a used oppo. There was a Yamaha BD player out there that according the the Yamaha site, is discontinued, but you might be able to find someone with some in stock. You are correct about optical and coax, if you play an sacd from those outputs, you are getting the CD layer, not the SACD layer.
On your second question, yes. Any player will do, it's up to your receiver to decode HDMI and supply the digital analog conversion. For new players, there are only two 'universal players, the aforementioned Sonys. They can both play DVD-A and SACD. There are some lesser Sony Blu Ray players , sub 100 bucks, that can also play SACD, but they are not universal and cannot play DVD-A. For example the Sony BDP-S6700 can play SACD and crutchfield has them for 98 bucks.
Edit: one note on receivers. Not all receivers do direct DSD to analog decoding and in the HDMI handshake with the player, the player will recognize this and the player will output PCM 88/24 or 176/24, but it is still multichannel. For example my anthem cannot do DSD decoding. I doubt you'd notice as 88/24 or 176/24 are still hi rez and very good formats.
On your second question, yes. Any player will do, it's up to your receiver to decode HDMI and supply the digital analog conversion. For new players, there are only two 'universal players, the aforementioned Sonys. They can both play DVD-A and SACD. There are some lesser Sony Blu Ray players , sub 100 bucks, that can also play SACD, but they are not universal and cannot play DVD-A. For example the Sony BDP-S6700 can play SACD and crutchfield has them for 98 bucks.
Edit: one note on receivers. Not all receivers do direct DSD to analog decoding and in the HDMI handshake with the player, the player will recognize this and the player will output PCM 88/24 or 176/24, but it is still multichannel. For example my anthem cannot do DSD decoding. I doubt you'd notice as 88/24 or 176/24 are still hi rez and very good formats.