(1) What mods do I need to use the CCCCC mod with Starbound?

(2) What other mods can this mod interact with?

(3) Are there any mods which are incompatible with this mod?

On principle, you can use this mod without the need for any other mods, however Base in a Box and Alchemical Reactions are highly recommended. 

Without these mods, a lot of the features of this mod may be unplayable.

• Many of the new custom devices you will find in this mod, with few exceptions, require the use of the Science Station or other crafting stations, particularly those from Alchemical Reactions.
• You can still scour the galaxy for various components and objects, but without the Science Station, a vast number of them cannot be crafted.
• The recipes for most items require reagents such as Powders and Essences from Alchemical Reactions, be it finding a colour glaze for pottery items, or a reagent to manufacture the ladles and the natural blocks that they can produce therein. 

In future, I may make new tweaks to the 1.4 Peacekeeper Bounty Hunting system to ensure greater access to these items, but at present I have no idea how to do it.

(4) Why are there non-Cyrillic letters under the Cyrillic heading for the Signage Press crafting menu?

Ask no questions and you shall hear no lies.

This mod was created with Frackin' Universe and Starbound Awakens  in mind. In fact, with regards to Starbound Awakens it can be said to be an "expansion pack" of sorts, given that it gives you new options with regards to producing Carbonite and Kyber Crystals. 

Other mods: 

• Castlevania :—  Some plants cannot be obtained from the Trader, they must be created using a Catalyser. Other items are breakables, others are treated as farmables. There is some interactibility with Alchemical Reactions - certain decorative items are converted under CCCCC into facsimiles of crafting stations under AR, while some decorative items require items from Alchemical Reactions in order to be crafted. The Save Point functions as a Mission Checkpoint.
  
• Universal Uncrafter :— With the adoption of this mod into CCCCC, the Universal Uncrafter has been given a new recipe - both the Alchemical Reactions and BiaB mods however must be installed along with CCCCC in order to access it. The addition of Universal Uncrafter also means that any version of this mod other than the original by Peasly Wellbott is now incompatible with CCCCC.
• Colony Tweaks, Tenant Pack :- Various NPCs, especially merchants, have had their available stock altered. There too are Felin, Fenerox and Mantizi versions of certain NPCs.

While a lot of effort is spent trying to make usage of CCCCC as stress-free as possible, any mod which changes vanilla crafting stations (ie Basic Oven, Crafting Workbench, Primitive Furnace, etc) has a chance of breaking this mod or resulting in adverse results.

• Craftable Natural Slopes :- Content from this mod conflicts with CCCCC over the use of block IDs. There are no plans at present to produce patches to mitigate this issue - we advise our subscribers to use the Dramatic Terrain mod instead.
• Build Your Own Ship (BYOS) :- This mod may interfere with BYOS and prevent access to some of BYOS' features. There is no plan at present to address this issue.
• CN More Farming:- Content from this mod series is said to be blocked if not impaired by CCCCC, but overall both mods are mostly compatible, ie will not cause crashes or immensely disruptive bugs.
• Wolf's Pottery Mod :- This mod is completely incompatible and will crash Starbound if both CCCCC and Wolf's Pottery Mod are installed.
• Universal Uncrafter :- All versions of Universal Uncrafter except the original by Peasly Wellbott must be considered to be incompatible.
• The Galactic Protectorate : - This mod is incompatible with both CCCCC as well as its submod, Nebulox'  Protectorate+ (now defunct). The incompatibility between both mods lie in that they have ID conflicts for items.