First post, sorry I am still lost. Basically your last piece of your request...:-)
1. Lookup field with +: When you start typing a name into a lookup field, it will bring up a list of the related names from the module where that lookup is linked to. So say you type Joe Soap in your new module lookup field from Contacts, if Joe Soap exists in the Contacts module it will show and you can just select the name, which will link the records using Joe Soap. If Joe Soap doesn't exist, you can create Joe Soap by clicking the + sign, which will open to quick create dialogue box effectively creating Joe in Contacts, as well as filling in the name in your lookup field once you Submit.
2. You mention multiple custom modules all with a full name. Thus I understand as a separate action once you selected Joe Soap in the one module and saved, the same contact must then be automated to be filled into the similar lookup fields in the other modules?. So as to avoid looking up the same name in each module? If so, depending on your setup you can use workflow with daisy chain attributes. I can help you also with this.
3. Observation issue: This sounds like its due to compulsory fields that need to be filled in, which might not only be the Full Name field. Remember, the Full name field is done by the system as a combo of First name and Last Name. The default X2 have various compulsory fields before you can save. (Red star next to field). If any of these fields aren't done it will give that warning. Sounds to me like when you create a contact using the + option from your lookup field, it might be that you aren't completing the compulsory fields, or they may even be hidden from the dialogue box thus you wont know about them. Personally I take off compulsory aspects on fields as they also screw up your forms to collect info.
Not sure I understand. Are you asking How to create a custom lookup field? or asking How to get other info from Contacts after you created the custom lookup field?
The info above refers to trying to create a custom field in your module. If so, the FIELD NAME is the name of the new field in your database. The ATTRIBUTE LABEL is what you see on your screen next to the field. TYPE, is Lookup and you select the module to lookup. (Contacts)
Then in your Form designer make sure to place the newly created field on the form to be used.
Using the field...in your module when you type something in that field, being a lookup field, it will try and search for the record by that name.
not sure what you mean. X2 can only show a module you are using and busy with. To see multiple views of areas in X2 why not just open another instance of X2 in a browser and/or use a multiple screen setup (which is what I do)??