No, however a combo DAC/amp is limited by the performance of both the DAC and amp and offers no upgrade path unless either the DAC has a line-level output to connect another amp or the amp has line-level input to connect another DAC. The combo provides the convenience of the single power input and usually a smaller footprint.
Separate DAC and amp provides the opportunity to upgrade either device independently, or to run multiple amps - headphone or speaker, solid state or tube, etc. - from a single DAC. It also enables the acquisition of the ideal DAC and amp for your use case, however this is rarely driven purely by sound quality for a given budget.
Yes, as long as the laptop has an available USB port and the DAC has USB input.
Usually "hybrid" refers to a solid state amp with a tube re-amp, however you appear to be looking for a combo DAC/amp under US$100. On that budget you might struggle to find quality options new, however the used market should provide some good options.
One option you should seriously consider is the
Radsone Earstudio ES100. It's a
balanced USB DAC/amp for under $100 which also supports Bluetooth 5.0 with LDAC, has built-in EQ so you can use e.g. a
Harman curve EQ for all inputs. It's tiny and light because it's designed for mobile use, but has features for a price which is a fraction of that for any comparable desk device. While it's not a power plant, it can drive your HE400i easily, as it did mine. You might also look at the very similar
FiiO BTR5 and
Qudelix-5K.
Radsone also has not-mobile
HUD100 for about the same price as the ES100. I confess I don't see the real advantage in almost any use case, but it's still a good option for buying new on your budget.