Answering the questions an order that makes sense to me:
Are the identified processes sensible, or are they too abstract?
The items on your process list are rather brief and looks to me more like scenario heading names than processes. As I read it, in 4+1 processes are essentially running programs.
... At the highest level, the process architecture can be viewed as a set
of independently executing logical networks of communicating programs
(called “processes”) ... 4+1view-architecture.pdf
The process view is a decomposition of the interactions between programs (presumably in accomplishing a scenario). It may take several diagrams of the same type and of different types.
So, you're going to want to identify individual processes (e.g. programs) that are interacting to complete the scenarios.
Does this imply that I would need to develop 8 sequence or activity diagrams?
Is it sensible and clear to make , for example, 8 separate diagrams, or one diagram covering all the processes?
Not necessarily. You will most likely need more than one diagram; however, you many not need exactly 8. After identifying the programs that are interacting (for each of the scenarios) you may find that several of them collaborate across two or more scenarios. For example, you may find you can show account lookup and authentication together on a single process view diagram (the interaction between client program, and several server programs).
Let's take a simplest possible example: you have two processes (programs) A and B. To show their interaction, you would use a single process view diagram (perhaps a sequence diagrams, but you might use communication or other as well). So, two processes that interact results in one diagram, if you will.
How should the implementation of the Process View be performed, using either of the two diagrams proposed?
First, as already mentioned, the key is to identify the processes (programs) that are interacting, and then create the process view(s) using diagrams to show those that interact (for a given scenario). I would suggest starting with communication diagrams, as these allow for showing interactions between components in an easy to read manner. If you need to show ordering of the individual interactions, then use a sequence diagram. The activity diagram should be held for subsequent detail. For one, activity diagrams don't indicate the "who" part of the interaction of the various steps of business logic (decisions, etc..), and in the process view you are trying to show, at least at the higher levels, the "who" of the interactions.
... Communication diagrams show which elements each one interacts with better, but sequence diagrams show the order in which the interactions take place more clearly. ... Communication diagrams, Wikipedia
As you identify the interacting components, keep in mind who is responsible or authoritative for what information. There does not appear to be lot of moral support in 4+1 for the information model, which I feel is a critical component of the architectural description of a system, that can be understood at a high level as who is authoritative and responsible for what content (and at a lower level can be elaborated in a more or less relational manner). For example, in an order system, the responsible component for accepting the orders is the same one that issues order id numbers, stores orders for later retrieval, the latter of which go to the information model and information responsibility aspect of the system.
Personally, I like Domain Driven Design, plus I add a higher level description of roles in the ecosystem. (Though I have also (had to) use TOGAF, which I feel is not the best but at least more modern than 4+1, IMHO).