What would happen if there was two more planets beyond Pluto, one with two times the size of Pluto and another with 4× the size of Mars, I'm curious to know what effects this would have on the planet close to the Sun, such as planets around the same position of the Earth, and what would happen to man kind?
And is there a maximum size a planet could be before it would start to affect the Sun?
The effects would be minuscule. How minuscule? Lets say the 4x Mars planet is orbiting at 50AU (pluto's furthest distance from the sun is 49.319AU). There are lots of ways to analyze this, but the most useful may be comparing it to be big fish in the pond - Jupiter. Jupiter is so much more massive than the inner planets and so much closer than the other outer planets, so it has a vastly huger influence on the inner solar system than any other planet (and it's influence is still not enough to destabilize the inner system).
Jupiter orbits at about 5AU. The force of gravity is proportional to mass, and inversely proportional to distance-squared. This planet is 10x further away, making the force of gravity at the Sun 1/100th as strong. Jupiter is 316 Earth Masses, Mars is 0.107 Earth Mass, this planet is 4x Mars, making it 0.428 Earth Masses, so Jupiter is 316/0.428 = 740 times more massive, this makes the gravity 1/740th that of Jupiter. The force of gravity on the sun is thus 1/74000th that of Jupiter. Because the inner system is on average very close to the sun, a similar force will be applied to them, Jupiter will be having about 80000 times more influence.
But can such tiny forces add up anyway? Kind of. In a similar way to if one person earns \$80,000 a day and a second person earns \$1 a day. If you start with something minuscule, it adds up to something minuscule.
If the planet was the size of Jupiter, it would still only have 1/100th the force on the sun. If it was 100 times larger than Jupiter the force of gravity on the sun would be equal - however at that mass it would actually be a star itself. Once a planet is 15 times larger than Jupiter, it is massive enough to start nuclear fusion and becomes a brown dwarf. So the short answer is at most it can be 15 times larger than Jupiter, but only because at that point it ceases to be classified as a planet, the gravitational influence on the Sun will still be slight compared with Jupiter.
It would be bad. The strong gravity (locally speaking), would destabilize the Kuipper belt, pummeling the solar system with comets. Even a 4x Mars might be bad out there if it just popped into existence, although 4x Mars is still pretty tiny, and there's a lot of space out there.
Planetary evolution theories currently don't allow a large (multiple Jupiter mass) planet to evolve so far from the sun. However if it had, I suspect the effect would be bad. The development of a environment supportive to life on Earth appears to have been in large part due to bombardment by watery comets from the outer solar system, which helped add water and other volatiles to the baked surface of protoearth. A large planet out at around Pluto's orbit might have acted like a comet vacuum cleaner. However a 4x Mars planet would not have been big enough to have such an effect as its influence would be utterly dwarfed by that of Uranus and Neptune. It would probably change the far outer system slightly, but would have no real influence on the inner system.
I haven't even bothered mentioning the 2x Pluto. Mars is already a tiny planet, Pluto is much tinier again, it is only 1/50th the mass of Mars. There are a number of dwarf planets out in the neighborhood of Pluto with a similar mass to Pluto, so the development of a 2x Pluto planet by a couple of these colliding together is not implausible, and it would basically have no effect whatsoever on the solar system.
In my analysis the influence of a 2x Pluto dwarf planet would be "none whatsoever" and the influence of a 4x Mars planet would be "almost none whatsoever" - in all cases the gas and ice giants would literally dwarf the influence of such tiny planets.
How far beyond? If just a little, the larger one would change the dynamics of the neighborhood and the Edgeworth-Kuipper belt would not be a thing. Which means Pluto would not be there either.
Large bodies "clear the neighborhood" and follow a generalized Titus-Bode "rule of thumb".
Planets won't affect the sun. Even if was large enough to be another star, that is a very common thing. What effect did you hqve in mind? If you mean making the sun wobble, it already does.
