One note: What is meant by "IR filter" depends on the context in which the term is used.
- When we say the camera has an "IR filter" in the stack of cover glass in front of the sensor, what we mean is that filter cuts IR light. That is, it blocks most of the IR light falling on it.
- When we talk about an "IR filter" that we put on the front of our lens so our camera can record infrared light, what we mean is a filter that allows IR light to pass and reduces how much visible light is allowed to pass.
The former and the latter are opposites, even though in common usage we call them the same thing!
Now that we've got that out of the way, let's see if we can answer your questions:
Will I face the issues like problem with focusing or the need to do long exposure in daylight and generally all the issues that you face with IR filters used on non-converted cameras?
You won't need to do extremely longer exposures in daylight. This is because an unconverted camera has a cover glass over the sensor which includes an IR cut filter that rejects most IR light. With that filter removed the sensor will be much more sensitive to IR light. The "IR" filter you put on the front of your lens allows IR through and reduces visible light, just as a "green" filter allows green through while reducing red and blue. You still will need to expose a little longer than you would for the same light levels if you were shooting visible light only, but it would be nowhere near as long as if there were an IR cut filter in the optical path in addition to the overall lower sensitivity.
Depending on the exact DSLR you're using, the light meter used when metering while using the viewfinder may or may not be accurate when measuring infrared light only. Older DSLRs have a single (monochrome) or dual layer light meter located in the area of the pentaprism and viewfinder that is more sensitive to specific wavelengths of visible light. Some newer upper tier DSLRs have RGB+IR light meters which would be more accurate with infrared light.
As far as focusing goes, it depends. If you want to use the viewfinder to compose your framing, which is dependent upon the dedicated PDAF sensor array, then yes, you'll need to do some compensation for using autofocus. If you shoot using Live View the camera will focus using the lens position that gives the highest amount of contrast in the image projected by the lens onto the main image sensor, so you won't need to do compensation for focusing.
Can I switch to IR only and full spectrum with on-lens filter?
If by full spectrum you mean a camera that is both sensitive to visible light and portions of the infrared spectrum, then yes. If the IR cut filter in front of the sensor is removed from your camera then it will be sensitive to both visible and IR light.
But the IR light allowed through to the sensor when there is no IR cut filter directly in front of the sensor will affect the color accuracy of light in all three cannels of the visible spectrum. This is because above 800 nanometers the 'red', 'green', and 'blue' filters¹ of the Bayer mask will allow IR light through all of them at pretty much the same degree of transmission.
This is the response of a fairly typical Bayer filtered sensor with no cover glass (nor an IR cut filter) in front of it.
Notice that the sensitivity of silicon based sensors are generally less sensitive to IR light than light in the visible (to humans) spectrum. But you will gain the even more significant benefit of no IR filter cutting most of the energy in infrared light before it reaches the sensor.
Of course when you put an "IR filter" (which reduces the amount of visible light allowed to pass) on the front of your lens you will no longer be collecting most of the energy from visible light so your exposures will need to be longer than if your were capturing both. But your exposures will still be much shorter than if your were fighting an IR cut filter on the sensor's cover glass as well as the reduction of visible light caused by the filter in front of the lens.
¹ The 'red' filters of a typical Bayer mask are actually a yellow-orange color. This mimics our retinal cones. Our 'red' retinal comes are actually most sensitive to a lime-green color of light! The 'green' cones are usually most sensitive to slightly yellowish green and the 'blue' cones are actually most sensitive to a violet-purple color.