The size of the frame will only start causing problems when it is larger than the allowed MTU on an Ethernet port. By default, an Ethernet port will allow an MTU of 1500 (without the Ethernet header) so 1514 with the header is no problem for the default.
For the purposes of the specific lesson, IP packet size of 1500 was deemed problematic for the MTU of 1400 just to get the point across. The possibility of fragmentation and the settings of the DF bit were not analyzed here in order to maintain the simplicity of the example. Notice in the wireshark capture that DF bit was indeed set, so the communication failed. Now whether or not fragmentation does or should occur when web browsing mainly depends on the configuration of the network in question. HTTP/HTTPS do not have any direct influence nor do they require any specific setting on the DF bit. This is determined by the specific networks that the packets are traversing.
I assume you’re talking about the MTU parameter set on the Ethernet interface. If this is the case, you can connect one switchport with an MTU of 1400 to a switchport with an MTU of 1500. Any frames that attempt to enter the 1400 MTU sized interface that are larger will be dropped. MTU size does not have to be the same on both ends in order for a link to function, unlike some other parameters like speed, duplex, trunk configurations and others.
Jumbo frames are those frames that are larger than the standard 1500 bytes. When a switch is configured to accept jumbo frames, the size of those frames are also specified. Any frame up to that size will be accommodated. However, keep in mind that a jumbo frame is a layer 2 concept. When this frame is then called upon to encapsulate an IP packet which in turn encapsulates a TCP segment, the packet and segment sizes must also be smaller than the maximum jumbo frame MTU.
UDP traffic does not conform to the TCP MSS configuration. UDP does not have a concept of MSS. UDP datagrams are fragmented based on whatever fragmentation the IP protocol can achieve. However, for TCP, MSS can be a solution as it will reduce fragmentation and is initially agreed upon at the three way handshake.
I hope this has been helpful!