Could you  please suggest a free efficient software tool which can handle

FASTA files?

G'Day Sarah: It really depends on what you want to do! FASTA files are very basic and can be transported into most DNA analysis programs - if not they can be readily converted (e.g., using http://genome.nci.nih.gov/tools/reformat.html). There are quite a few free software tools, including those on various companies' websites. If you want to look at simple restriction enzyme digests EnzymeX is very easy to use. A somewhat outdated program that has more 'bells and whistles' is DNAStrider (for Macs). I like SerialCloner (e.g., vs 2.6.1) which is Mac- and PC-compatible. I would imagine others on this site have their own favourite tools.

For alignments and tree building ClustalX is the usual goto standard, though modern databasing software like Geneious has far outstripped those basic tools.

There are literally hundreds of online tools scattered throughout the web. Have a look at expasy, a catalog of tools with links. Fasta is a standard format and most tools accept it.