Let us answer your queries in logical order:
1. Normally Service Tax is payable by the person providing taxable service. However, for specific services, Service Tax is payable by the person receiving such services. This mechanism is called reverse charge (vide Sec. 68(2) of Finance Act). GTA means Goods Transport agency service.
When a specified person (any factory, registered society, co-operative society, dealer of excisable goods, body corporate, partnership firm) receives the services of transportation of goods through a goods transport agency, then such person is liable to pay Service Tax @ 12.36% on 25% (subject to the trasporter not availing input credit on inputs, capital goods and input services) of the value of the invoice issued by the transporter, subject to certain exemptions (up to Rs. 750 per consignment and Rs 1500 for all the consignments in a goods carriage) as to the value and nature of goods (fruits, vegetables, eggs or milk).
Hence effectively, Service Tax payable under reverse charge (GTA) comes to Rs. 3.09 for an invoice value of Rs. 100.
2. As per rule 2(d) of the Service Tax rules, a specified person receiving the service of GTA is the person liable to pay service tax. As per Section 69 of the finance act, every person liable to pay service tax, has to necessarily register themselves under Service Tax and pay the service tax electronically.
With effect from 1st October 2014, every assessee making payment of Service Tax has to mandatorily make the payment electronically.
Before paying Service Tax under reverse charge as stated above, the service receiver needs to obtain registration under service tax under the category of "service recipent" for the service of "Transportation of goods by Road". Please refer to the FAQs on Service Tax registration as isued by CBEC, as per this link:
https://www.aces.gov.in/Reg_FAQ.jsp.
3. Cenvat input on services is similar to cenvat credit of excise duty on inputs used for manufacture, where service tax on the services provided is paid by utilizing the service tax paid on the services utilized for providing the service - referred to as output service.
4. However, in the case of GTA as stated above, the definition of output service is amended to provide that where service tax is payable under reverse charge, such service cannot be termed as output services. Hence service tax for services covered under reverse charge has to be paid only in cash. Cenvat Credit cannot be utilized.
Hence, considering the above, if your entity is liable to pay service tax under reverse charge under GTA service, please register yourselves under service tax. Please refer to the link as above for any assistance in this regard.
I hope this clarifies your query.