Raw reads: Is this the total reads present in the fastq file? So a paired-end sequencing has two files which means I'll add the total number of reads from both the files to get this number?

Correct. Each cluster (in Illumina) produces those two reads from two ends of each library fragment. Paired end reads are in separate files so you don't need to add those numbers. Each unique cluster produces two reads in paired-end sequencing.

Clean reads: Is this the number of reads I get after the quality control step? Is this also the combination of both the files?

Paired-end read files are qc'ed and scanned/trimmed together so the read number in both files should remain identical post-processing.

total mapped reads: I believe this as all the reads mapped to my genome.

Some reads may have secondary/supplementary alignments (multi-mapping) so the number may look larger than actual number of reads.

unique mapped reads: ?

Like what it says. Reads mapped one time in genome as pair.

Also, for publishing ChiP-seq data what are all the essential statistics including/apart from the above?

Probably nothing in the list above would need to go in a publication. This is part of standard analysis.

With ChIPseq you expect to see a lot of duplicate reads since you are enriching for regions in the genome.