Will your other device have the same issue? You may adjust the extender to a different location to check whether the issue still happen.

For your second question, did you set the extender to a static IP address but with the DHCP server on?
Sometimes if the extender fail to ping the router's DNS or IP, it will show no internet access but with internet because some router block ICMP ping function.

Yes, all connected to the extended network. The source gives a full 20 Mbps speed even though at the edge of reception with barely one or two signal bars. When connected to repeated network with full signal bars, the speed is capped around 2 Mbps; the repeater is half-way. The status pages shows constant good signal for the 2.4 GHz source network. 5 GHz is turning weak (red) at times, and I've turned it off on both devices for the time being.

I would find any blame finding in the placement unconvincing, as simple reboot clears this problem. After the reboot process the operation is immediately always back to full 20 Mbps speed. Thinking about it I can say yes, the repeater has most probably experienced the speed drop during day time at least a couple of times, likely during some unutilized times.

For the second question, yes. I had to set static IP, as the default IP wasn't in the router DHCP issue range. Is there a performance or function impairment known or expected? Anyway I just changed the router IP address to cover the repeater issued default address. Now the status says Internet is connected.

For your first question, I suggest you to contact tp-link support at support@tp-link.com for help.
I don't think there is a performance impairment to leave the extender with a dynamic IP address.

Thanks @vieldcs for your answers on the topic. I think I'll have to do that, although I'm in a bit of an awkward situation with this, as I've gotten the repeater as a present and I'm not really in a position to ask for the proof of purchase which wasn't included. But I reckon TP-Link will be reasonable with my request, as there's a 3 year warranty sticker on the retail box and the product has been on the market for less than that, and it's clearly in a mint condition.