Feasibility reports come under the BABOK's Enterprise Analysis section (Chapter 2 of version 1.6 www.theiiba.org)

Basically a feasibility check discovers whether a particular solution (a) meets the needs of the project/problem and (b) is do-able within the constrainst of the organisation.

"Meeting the needs" is done by defining the business objectives and breaking them down into specific things (eg measurable results or tangible products) and then assessing solution optins to see of the particular option will deliver the goods.  Think of a shopping list of features mapped against product specifications.  If having an FM radio on your MP3 player then an Ipod fails your feasibility check.

"Do-ability" addresses contraints.  You only have $25 for an MP3 playr?  You aren't getting an Ipod. Your company has specific IT standards that are required?  Maybe Linux doesn't meet tose standards, etc.

2. Suppose a client gives me his requirement, can I confirm the deadline given by the client without consulting the technical people or Should I collect the requirement  from the client, discuss the same with the technical people (software developer) and then give a conformation to the client?

Usually you rely upon others to do the technical delivery, and in those circumstances you will consult with them prior to making deadline commitements.  As a BA you will usually refer to the PM for schedule and budget related issues. If you are referring specifically to timelines on work you, or your team, will deliver you can give your estimates.  Unless you are highly experienced always consult with others first.

Project budgeting can do, but not usually.  BAs may be asked to provide estimates on the effort they (and their team) will put into the project, which will have budget impacts.

However, BA's are often asked to develop a project's business case which analyses costs and estimated project benefits.  As part of this you will pull together various budget elements of the project to fully understand the costs.  Usually you will extract forecast benefits from subject matter experts.  If you don't have good financical analysis skills, don't worry too much.  In larger organisations there will usually be financial analysts around to help.

4. What is that we are supposed to do  as a BA?

The key skills are faciliation and communication.  Each organisation has it's own ecpectations.  Large organsiations tend to use models like PMI's PMBOK or OMG's PRINCE2 (which are the frameworks that the IIBA's BABOK refers to.)  In Agile projects the BA's role is more akin to the client's advocate and quality manager.

5. What are the problems that we would face as a BA and how do we overcome it ?