That fuse panel has to be +40 yrs old, I think it is time to replace it, since buss and fuse connections deteriorate over time. And you may not have add a sub panel, but if it is for a different location, it will be much simpler with a new breaker panel.
While 120/240 volt sub panel are certainly the norm, I do not believe there is a specific prohibition against a 120 volt sub. If you proceed, I would plan on the ultimate use of this sub, and provide a panel and cabling (4 wire feeders with enough slack to move to new main panel) based on the ultimate use. Also insure the neutrals and grounds are kept separate in the sub.
A single phase panel has 2 hots and a neutral, the term "2 phase" is kind of confusing. Your picture shows a single phase panel. Two phase power generation is basically obsolete, but 2 phase is sometimes used for control circuits in 3 phase systems. At any rate, what comes to your home is single phase while some commercial power is 3 phase.
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