Should my web agency have different rates for design, programming, SEO, etc?

Absolutely!

Apart from anything else it gives you more flexibility when outsourcing, or to charge less for things that either the client won't pay as much for, or you're less skilled at.

To my mind it looks more professional if the invoice has £xx for copy writing or admin, and 2x£xx for programming and design.

Just remember to put enough in your lower rates to cover your own overheads

I certainly think it makes sense to charge based on the complexity of the service.

Surely you don't have a team that is 100% cross-functional and effective in all those areas (if you do, I'd like to meet the UI guy that also does database programming and SEO).

Setting different rates for different services also communicates to your customers that not all functions are the same. I think it is helpful for people to understand that different portions of site design and marketing jobs have different complexities (and thereby rates).

Yes.

Differentiate your rates based on three key factors:

1. Where you have the best / strongest skills
2. Your ability to add value to your client over and above what they could do on their own or with another provider
3. Local market rates for comparable skills

If you have a superb SEO person, for example, who can have a significant impact on improving completed transactions for a client, this is worth more than a basic copywriter.

In addition, you might consider some fixed price packages in which you bundle a defined set of services and tie these to a fixed outcome for your client. Can be better value with a more predictable cost to your client and can increase your margins in the process.