If I wish to sell put options to collect the premium, are there advantages of setting a time to expiry of 56 days as opposed to 30 days? Does this lower the risk? Here I am considering American style options.
Option premium decay is non linear so you receive more premium per day for writing nearer term options. For ATM options, a loose rule of thumb is that the premium for ATM options is related to the square root of the time remaining. In general, that's why writers tend to sell nearer weeks/months and buyers tend to buy further out weeks/months.
A nearer expiry exposes you to less time risk.
A further expiry brings in a larger total premium so in terms of dollars, it has less risk. In terms of time exposure, it has more risk.
Note that a pending dividend and skewed IV due to or imminent news can distort this relationship.
Does this lower the risk?
How do you think extending the period someone would possibly use your put option to sell you something at a predetermined price would possibly logically lower risk? This makes ZERO sense. The longer the period, the higher the risk that the price goes against your wishes.
Are there any major advantages of selling put options with a longer expiry date?
You get a higher premium.