Brand Design

No, but a website will borrow its colors, type and spacing from somewhere. If that somewhere is whatever was at hand, the site reads as assembled rather than designed. Doing the logo and design system first usually costs less than reworking a finished site later, and if you already have a brand, the work here is more often tidying and documenting it than starting over.

The files you need. The logo as a vector artwork plus the raster exports it needs, the type system, the colour values, and a short guideline document covering how the pieces are meant to work together. Enough for a printer, a developer, or the next designer you hire to stay on-brand without asking me first.

Yes, and it is often the better starting point. I would keep the logo and build the system around it. Following your already present and established visual identity, using your type system and already present color palette. If the logo itself could be improved I could suggest a re-design, but if it is fine and there is no need, we can keep it as is.

Yes, it will! That is where most logos fail, so it is part of the work rather than an afterthought. I test the logo at favicon size, as a single ink colour, over a photograph and look to make adjustments so the final result is something recognizable.

Usually from one week to three weeks for a full identity, longer if naming or positioning work is in scope too. The length is mostly set by how many rounds of feedback you want, and by how quickly the people who have to make the decisions can make them.

No. The same rules have to hold on a business card, an invoice, a pitch deck, an app icon and an advert, which is the point of building a system instead of a single graphic. The website is one surface of a brand, not the whole of it.

I can understand the attachment to something we ourselves have created. But using AI-generated logos is highly inadvisable. As an alternative, I can suggest designing a logo based on the logo you have already generated; that way, you have a vector-based logo which can be scaled and sent to print, and rasterized as well if needed.