Paired ends is a configuration in sequencing platforms. Illumina is the most popular at the moment and most single-cell sequencing is done using paired-end Illumina sequencing. It varies between single-cell technologies but most 3’ scRNA-Seq protocols use paired ends.
Kallisto is a tool for handling raw data. Many databases supported processed data in BAM format or UMI/read counts. You should not need to run kallisto unless you are involved in handling raw data from sequencing performed by your laboratory. Some databases such as SRA and EGA support raw data in FASTQ format, others do not for ethical reasons or the data is too large.
I recommend downloading from SRA via their command line interface (this is documented on their website). It is possible to extract paired ends from an aligned BAM file using bedtools and samtools. I’ve done this with the Macosko et al (Cell 2015) DropSeq data for example.
Note that in some cases, the barcode is stored in databases as the headers of the FASTQ, BAM, BED, or CTSS file rather than a separate read. Single cell transcriptomics is an emerging field so there isn’t a standard way to do this, it varies between labs and data centres. For single-cell specifically, some databases are being set up, for example: https://data.humancellatlas.org/