Electrical – Should exterior receptacles be on a separate circuit from interior receptacles

The outdoor receptacle will have to be GFCI protected.

NEC 210.8 At dwellings, ground-fault circuit-interrupter (GFCI) protection shall be provided for all receptacle outlets installed in bathrooms, garages, grade-level portions of unfinished accessory buildings, crawl spaces, unfinished basements, kitchen countertops, wet-bar sinks, boathouses and outdoors. Receptacles that are not readily accessible may be exempt from the GFCI requirement

The receptacle will also have to be contained in a weatherproof enclosure, and if something will be plugged in for extended periods (Christmas lights for example) the enclosure should be labeled as "watertight while in use".

NEC 406.8 15 and 20 amp, 125 and 250 volt receptacles installed outdoors in a wet location shall have an enclosure that is weatherproof whether or not the attachment plug is inserted

It should not be a problem branching from an interior circuit, but you'll want to seal the hole where the cable enters the house to prevent moisture from entering.

As far as the NEC is concerned, there is no limit to the number of outlets (lighting outlets in this case) that are allowed on a single circuit assuming that the attached fixtures don't exceed the rated capacity of the circuit.

However, @Edwin raises exactly the correct point in the comment - what matters is what the fixtures are rated for, not what they are currently being used for. The general rule of thumb that electrical inspectors tend to use is around 8 boxes for a 15A circuit and 10-12 for a 20A circuit. Keep in mind that they are counting boxes, not what gets put into them. The idea is that you can put in a receptical rated at 5W, decide you don't like it, and throw something with a 150W load in the same receptical. The only thing that makes something a "light" in the eye of the inspector is that it is on the ceiling and has a switch running to it.

Outside of the load consideration you actually bring up a good point in the question, which is safety. While the NEC doesn't specify a minimum number of lighted branches (other than the panel lighting requirement), your local authority very well could. I know my jurisdiction only allows 2 rooms to share the same branch for lighting purposes, precisely for the reason you mention - you pop a breaker, you're in the dark.