Josh,
Verify whether you have the 25A (with 3 carbs) or the 25B (with ECU) so you get the right parts. Also get the Factory service manual, so you understand how everything fits together.
The last numeric digit on a Tohatsu part is usually a revision to the part since it was first manufactured; so the -1 part is a superceded part. The M designation isn't significant to the consumer, just the factory.
You will want drag link H, which has the 1 at the end of the part number. Yes, this is the link that connects the engine to the teleflex-style steering cable.
The ECU is the "computer" (electronic control unit) for the motor. The RC configuration requires a different cable to connect the ECU. Again, verify your model/serial to determine which bits you will need.
Yes, any Morse-style control will operate the shift and throttle (only - not ignition, start, etc.); Just be sure you don't get F and R reversed (pull for F vs pull for R). The Tohatsu controls are priced similarly to other OE manufacturers (in fact below many), and you will want the correct RC box for your motor, so that you have the correct power/signal wiring connectors for the motor. That way, you get the key start, kill, etc, and proper wiring for T/T, etc. As an alternative, you can connect a "divorced" key switch (separate from the RC box), and if you select the correct key switch (Tohatsu has them), it will include the ignition kill function. Ditto for the tilt and trim.
There are several different Tohatsu RC boxes. Some part number differences are just for paint color, but as I noted, you will want the one that has the correct wiring connectors, unless you will be hacking into the wiring to get the functions you want.