How can I disable the softkeys on the Polycom phones? What about the on the phone Do Not Disturb feature?

Check out the following page:
How To Disable Default Softkeys And "Do Not Disturb" Feature

How can I add custom Ringtones to Polycom phones? 

Check out the following Polycom Phone Customization page:
Custom RingtonesHow To Disable Default Softkeys And "Do Not Disturb" Feature 

Polycom: I've got inconsistent results with speed dials: sometimes they would not appear on the phones.

The phone reads this directory file during a reboot and/or restart. However, the phone does not read the file on an Update Configuration/CheckSync/HTTP reconfig event unless the permission on the directory file is set as readonly dir.local.readonly=”1”.

You can go to: {phone} > Directory resources and check dir.local.readonly. Add/edit/remove speed dials, Save and update phones (or send profiles to phone) and phones would pick them up (after reboot or not depending on firmware and model).

Note that speed dials with subscribe to presence checked would not appear on the phone if RLS is disabled. 

Also if the directory file is too big, it won't load. Check out this post from the Polycom community forums: http://community.polycom.com/t5/VoIP/Directory-Limit-100k/td-p/28184

I don't get missed calls on my Polycom

Make sure server side missed calls is disabled and missed call tracking is enabled.
You'll find both parameters in Devices > Phones > Lines > {Line} > Call Handling 

I have inconsistent results using DHCP on my phone

Make sure you don't accidentally have more than 1 DHCP server reachable by the phone (e.g. you might use a router with DHCP enable and enable also sipXecs DCHP). Also note that settings received from DHCP override settings on the phone, at least for Polycom phones. (For instance, your DHCP set some DNS servers but you want to use a manually configured DNS and input it on the phone TUI, the phone settings will be overridden by the setting from DHCP.) 

Why would my phone not reboot if I press "Restart" or even "Send profiles"

Check this page: Have Phones Always Reboot on check-synch

I have something like this in log, what do I do?*

May 23 10:30:57 localhost in.tftpd[3687]: RRQ from 192.168.10.152 filename 192.168.10.2/2345-12375-001.sip.ld
OR
May 23 10:30:57 localhost in.tftpd[3687]: RRQ from 192.168.10.152 filename some.domain.com/2345-12375-001.sip.ld

* The phone might not be able to provision properly.

This may appear in syslog with enlarged verbosity, or in the phone log.

On the phone check the Upgrade server setting (Advanced > Provisioning server > Upgrade server). You might have input by mistake something there and the phone tries to download sip.ld from the server.
It is good to know that it would try to pickup that file even before hitting <MAC>.cfg

We recommend to use that setting with caution and only if you're sure you know what you're doing!