Can Spells Be Cast While A Web Spell Is Active?

Casting a spell as a bonus action and another as an action in one turn is possible, provided that the conditions are described on PHB p.202. One spell has a casting time of 1 bonus action, and the other spell is a cantrip. There is no rule that says you can cast only X number of spells on your turn, but there are some practical limits. The main limiting factor is your action, as most spells require an action to cast.

Some spells, including those cast as rituals, require more time to cast, and when you cast a spell with a casting time longer than a single action or reaction, you must spend your action each turn. The rule permits you to cast creature spells at specific times, but it does not prohibit you from casting the spells at other times.

An entangled character who attempts to cast a spell must make a Concentration check (DC 15 + the spell’s level) or lose the spell. Otherwise, a creature’s casting and attacks are unimpaired by the web spell’s effect.

A restrained condition doesn’t prohibit any actions, except for movement over distance. Any spell can be cast while restrained, and web doesn’t force a DEX save on cast. Conjuring a mass of thick, sticky webbing at a point of your choice within range fills a 20-foot cube from that point for the duration. You must use a bonus action on your turn to cast the spell, provided that you haven’t already taken a bonus action this turn.

There’s no restriction unless the spell casting description requires movement. Being restrained isn’t the same as being incapacitated. Anyone in the effect’s area when the spell is cast must make a Reflex save, and if this save succeeds, the creature is entangled but not prevented from moving.