The correct weld size is based on the thickness of the branch pipe wall and the particulars of the piping code you are working with. The size will vary from one piping code to the next. The need to post weld heat treat is also dependent of the particular pipe code you are working with.
Whether you use stringers or weaves and any limitations on the weave is dependent on the piping code with regards to the need to meet Charpy Impact requirements. If CI is a requirement, you will have to control the heat input, which in turn will determine whether stringers or weaves can be used. The travel speed is the parameter most affected by the decision to use stringers (low heat input) or weave beads (higher heat input). Section IX nor the piping code will typically limit welding to either stringers or weaves. That is a decision that should be made based on the parameters used when welding the test coupon that passed all the requisite tests and recorded on the PQR. The WPS for production should be based on the "lessons learned" when welding the test coupon that passed all the required tests per Section IX and any modifications required by the particular piping code you are using.
Best regards - Al