The orbit depends on the mass of the central star and the distance from it.
A small sun with a low mass can enable a habitable planet to have a short orbital period, larger suns can enable longer periods. Can also change the energy output if you want your planet to be habitable, for example our sun with a higher energy output might make a planet with the distance of Mars habitable for humans, which has an orbital period just short of 700 days.
Since you have a specific star in mind and want and earth-like planet, you can probably calculate/look up the goldilocks zone (centered at around 1.87AU according to quick googling, but there might be something more detailed out there), where life as we know it is possible, and pick any distance in that zone to calculate the orbital period with the formula T = 2 x pi x sqrt(a^3/µ), T being the period, a the semimajor axis (radius in your case), µ = GxM = gravitational constant*mass of the star.
The rotational period can be affected by a moon, but there really isn't any restriction to it.
You can literally take your pick - tidally locked to the central star, short day/long year like Earth and Mars, more than a year and reversed rotational direction like Venus, huge planet with an extremely fast rotation like Jupiter (~10 hours, through a telescope you can see that it has a roughly ellipsoid profile due to the centrifugal forces).
Don't know what you mean by changes in "obliquity" in this case. There wouldn't be any issues with irregular orbits since it is't a dual (or more) star system, but an elliptic orbit is possible. That's your decision, though.