That’s really up to you. The default synapse is an exponential synapse with a \tau value in Nengo is 0.005s, and this is based on the (average-ish) synaptic time constant of the AMPA neurotransmitter. You can definitely change the synaptic value (and indeed even the synapse type – e.g. to an alpha synapse) to whatever your model requires. As an example, the Nengo integrator example uses a 0.1s exponential synapse. This value was chosen to be in line with the longer time constants of the NMDA neurotransmitter. My old research lab has a table of neurotransmitter time constants that serve as a decent reference for values.
That is correct. Weights can also be set manually. 
This forum post has a description and a link to the Nengo documentation on connections. These two sources provide a good explanation of the different types of connections you can create with Nengo objects.
But to briefly answer your question:
Connecting to an ensemble means that the signal gets passed through (multiplied with) the neurons’ encoders (this is described in the NEF algorithm) before being used to compute the neurons’ activity function. Connecting to a .neurons object means that the connection is being made to the neurons directly, bypassing the neural encoders.
This answer has a bit more nuance to it, and it depends entirely on what object the connection is connected to. If the connection is to an ensemble object, then both the transform and the function serve to inform the connection weight solver with information on how to solve for the connection weights. I go into detail about how this works in this forum post. To quickly summarize that post, the transform parameter instructs the solver to solve for decoders that perform a scalar multiple. On the other hand, the decoders serve as “one-half” of the full connection weight matrix of a Nengo connection. The “other-half” are the encoders in the post population. If you do a matrix multiplication of the decoders and the encoders, you’ll get the full connection weight matrix.
If you are connecting to a .neurons object, however, the transform parameter gets treated like the input weight matrix to the post population. If both the pre and post objects are .neurons, then the transform parameter essentially becomes the connection weight matrix.