The impression I get is that the main time openreach (the part of BT that handle the physical lines) care about customers messing with their incoming telephone wiring is when they are looking for an excuse to blame a fault on them.
As for engineers coming to install broadband it depends on what type of broadband you are ordering, there are basically three types of "broadband" that can be delivered by openreach.
Traditional ADSL/ADSL2 (any package with an advertised "up to" speed of 24 Mbps or less is almost certainly this). This is pretty much always self installed nowadays (in the very early days it was engineer installed and I wouldn't be suprised if this option still exists in theory but if it does it's certainly not a widely advertised option). It's up to you to install suitable filters to prevent the phones interfering with the broadband signal, the ISPs promote use of individual "microfilters" on every phone because that is the easiest method for idiots to understand but if you can understand phone wiring then centralised filtering is a better option.
Fiber to the cabinet with VDSL from the cabinet to the premisis (packages with an advertised "up to" speed of 40Mbps or 80 Mbps or thereabouts are most likely this despite being misleading advertised as "fiber"). In this case BT will install an "interstitial plate" between the back and front parts oft he NTE5 master socket and will usually install the VDSL modem nearby. The phones connect to the front plate of the NTE5 as normal, the VDSL modem is normally plugged into the interstitial plate but there are also a pair of terminals on the back of the plate to allow it to be located elsewhere. While installing the interstitial plate openreach may replace the complete master socket if it's an older design (including older versions of NTE5). They may also move the master socket if it's not practical to install the VDSL modem at the current master socket location.
Fiber to the premisis (currently I belive any package with an advertised "up to" speed of 100 Mbps or more is FTTH). In this case your existing phone wiring will become completely redundant and new fiber will be pulled in which will terminate in a box known as an ONT (optical network termination). Your phones and router will then connect to the ONT.
As for engineers coming to install broadband it depends on what type of broadband you are ordering, there are basically three types of "broadband" that can be delivered by openreach.
Traditional ADSL/ADSL2 (any package with an advertised "up to" speed of 24 Mbps or less is almost certainly this). This is pretty much always self installed nowadays (in the very early days it was engineer installed and I wouldn't be suprised if this option still exists in theory but if it does it's certainly not a widely advertised option). It's up to you to install suitable filters to prevent the phones interfering with the broadband signal, the ISPs promote use of individual "microfilters" on every phone because that is the easiest method for idiots to understand but if you can understand phone wiring then centralised filtering is a better option.
Fiber to the cabinet with VDSL from the cabinet to the premisis (packages with an advertised "up to" speed of 40Mbps or 80 Mbps or thereabouts are most likely this despite being misleading advertised as "fiber"). In this case BT will install an "interstitial plate" between the back and front parts oft he NTE5 master socket and will usually install the VDSL modem nearby. The phones connect to the front plate of the NTE5 as normal, the VDSL modem is normally plugged into the interstitial plate but there are also a pair of terminals on the back of the plate to allow it to be located elsewhere. While installing the interstitial plate openreach may replace the complete master socket if it's an older design (including older versions of NTE5). They may also move the master socket if it's not practical to install the VDSL modem at the current master socket location.
Fiber to the premisis (currently I belive any package with an advertised "up to" speed of 100 Mbps or more is FTTH). In this case your existing phone wiring will become completely redundant and new fiber will be pulled in which will terminate in a box known as an ONT (optical network termination). Your phones and router will then connect to the ONT.