Facebook – is it possible to disable comments to posts or hide comments made by friends from other friends

You could block the respective user(s).

If I share mutual friends with the user I am blocking, will they be able to see my comments to this mutual friend?

Blocking allows you to prevent most interactions with someone on Facebook. People you block won't be able to find you in searches, view your profile, or contact you with pokes, Wall posts, or personal messages. In addition, they will not be able to see your Wall posts, comments on mutual friends’ Walls, or that you are a member of the same group as them.

However, this might not work in certain situations:

Why am I able to see content added by a user that I've blocked on the site?

Blocking a user will prevent any type of direct interaction between you and that user. However, for technical reasons, there are certain instances when an individual you have blocked from your account may be able to view your comments on the site and vice versa, including comments on a mutual friend's photo. Please be assured that your listing will appear in black text, with no profile picture visible or contact links available.

There are a couple of settings you can adjust to change what and the order in which you see content in your news feed. In Facebook's Controlling What You See in News Feed the first method suggested is changing how you sort stories in your news feed (in your case you would probably want "Most Recent" to see stories from all of your friends in order of recency):

Use the Sort menu in the top right of your News Feed to choose which stories you see first. Click Most Recent to see stories in the order they were posted, or click Top Stories to see the most interesting stories at the top of your News Feed.

You can also Filter by friends list (which it sounds like you do not want to do, so make sure this isn't selected) Filter by friend lists

Click one of your lists on the left side of your home page to see stories just from the people on that list.

As you mentioned you can also hide or unhide stories.

You may want to check to make sure your settings include all stories since some users seem to have only close friends selected by default (see Facebook Changes News Feed Settings, Some Users Only Shown Close Friends by Default) I should note, however, that I wasn't able to find the interface shown below, so these adjustments likely are made in the previously mentioned sidebar where you can select sub-lists of friends

For the new news feed layout (circa April 2013 according to Mashable's How to See EVERYTHING in Your Facebook News Feed) the interface looks like this: