Here's a few things to keep in mind regarding those shops:
First, there is A LOT of demand for phone and web shops. Dozens of shoppers request each one within hours of the shops being published. Schedulers then review the requests and approve those that are from the most reliable shoppers and that are for the nearest dates (if for example you can request them for any day next week, the first ones to be approved will be those requested for Monday - so make sure to request the soonest dates).
Second - Badges. If you do even one of them, you'll get a badge proving you've had some experience in doing them before, making it more likely the schedulers will give them to you in the future. If you keep doing them, your badge level will increase, and the schedulers will, at a glance, see you've had extensive experience - and be very glad to give them to you again. Of course, new shoppers are not left out, and are whenever possible, given a chance to start off and earn some experience in every type of shop.
You can also try emailing or calling the MSP that posted the shop, and letting their schedulers know that you have requested it and would love the opportunity to do it - it's not guarantied to work, but it's a small extra step you can take if you want to, and that sort of engagement is greatly appreciated by schedulers, and often rewarded. :)
I hope this helps!
Self assigning and requesting a shop are basically done the exact same way - requesting only has that one extra step where schedulers review and approve the request before the shop is assigned to you.
Once you log into iSecretShop, go to the "Available Shops" page, and browse the shops that are posted. When you see the one you are interested in, you click "View Details" and it will open a pop-up window with all the information on the shop. Then, you can either self-assign that shop, or click "Request shop" to submit a request for a specific date. The schedulers are frequently reviewing these requests, so it should be approved soon.
Once you have a shop assigned to you, you can always view it on the "Assigned Shops" page - there you can see all shops you have assigned, and can click "Complete Shop" on any of them to see the full shop information, the shop instructions, the questions, or/and fill out the shop report.
In case of web/telephone shops, it's the same as any other shop - you can request or self assign them for a specific date (although usually those have to be requested, since there is A LOT of interest in them), and on that date, you do the shop and submit the report.
The simplest and fastest scenario would be that, for example, you self-assign a telephone/web shop today, and pick today's date when self-assigning it, so you can immediately just do the shop and then immediately just complete the report. 15-20 minutes effort and you're done. :)
A much more realistic scenario is that you'll be seeing those shops posted on Monday or Tuesday for the following week, not the current one, and they might only be able to be requested, not self-assigned. So within a day or two, you and 20-30 other shoppers will submit your requests for them, and the schedulers will pick the appropriate ones and approve, and if the shop is assigned to you, you would have to wait for the scheduled date on the following week to do the shop and submit the report. Still the same amount of time and effort, but a lot of waiting involved. :)
Well, it could be several options - that it was a "weekday" shop with instructions for the business days, but the available dates have been extended on to weekends (in which case it's okay to do on a weekend), or the MSP didn't block Sundays as an available day on which the shop can be done when they were posting the shops, or new shops for all days (including Sunday) has been created but the instructions and available dates were just copied from a previous shop that did not allow it to be done on Sunday, etc.
It is always good to contact schedulers when in doubt, but in this case it's necessary, as they are the only ones that can give you the correct information when there is conflicting info like this.