Hi,
There are a few ways to approach this scenario dependant on your requirements.
Typically, what you have presented so far would suit an SBA (survivable Branch Appliance) in your remote office. Naturally I'm assuming you already have a central lync site at your main office.
An SBA will give you a local registrar for users at that office, an embedded mediation server, and a gateway solution for PSTN connectivity.
You can terminate your E1 lines on the SBA, but should also consider moving to a SIP trunk instead of E1 as this would be a good time given you are looking at deploying voice there.
The gateway (SBA) will sit between your existing PBX and the PSTN, and all call flow will pass through the gateway to the legacy PBX.
By having this SBA, your branch users will be able to make external calls and operate within their own office even if their link (WAN) to the main office goes down. There will however be some limitations such as response groups and conferencing which will
rely on the Lync FE at the main office.
With this SBA you are free to peel off and migrate users over to Lync at your own pace, all the time allowing call flow between systems and with the external PSTN.
In answer to your questions;
1.) It is prefered to use a gateway, but you could have direct SIP between the Lync and the legacy PBX (inter trunk routing).
2.) Users at the branch office would be registered against the SBA in the branch office. I don't understand the management question entirely, you can manage them from the Lync FE at your central office or the SBA at teh branch.
Quite a generalised answer to a broad scenario, but I'm happy to answer more specific questions you might have.
Kind regards
Ben