Is it possible to implement hr without fico in any company? If yes, then who will create the company and other things in enterprise structure. if my company is implementing only hr without fico and in hr also only personal administration is it possible?

It is very much possible to implement HR(PA) without FICO. But it sounds very odd that the company wishes to implement only HR & that too only PA. What about other modules ? If you want other modules like MM / SD you will definitely require FICO. Utilitiwise its really absurd if some company only want to use HR(PA).

It is not madtadtory to have FI/CO or other module while implementing HR but it is required to maintain the min. config while going for the HR whereever having the integration. So the basic config such as company code, cost centre, Business Area, etc. may be maintained by the consultation of FICO counter part

For the second part of your question, YOU, the HR guy, will create minimum information in FI and maybe CO (company code, maybe cost centers). Just create an IMG project for PA HR, and the needed basic FICO activities will be included.
*-- Battacharya

What are:
1. cost center and work center.
2. personnel area(WERKS) and personnel subarea.
3. Retrocalculating Account.

Cost Center is for assigning Symbolic acounts related for Posting in GL Accounts and Work center is related to specific work area as Utilities, Boiler section, Processing section and Others you can assume.

Personnel Area is an exact Geographical Location under which the comp decides to run their Processing and Personnel ares are all as the Departments in an Hierarcheal Structure which are divided for TIme mgmt, Payroll as PS grouping.

Retrocalculating Account. --- > First it is not Retrocalculating Account and it is the payroll which is the running in this month has to carry any earliest payroll for balancing and controlling the payments for an emp for and can be used while paying any Bonus or advance.