The way I see it, the problem is two-fold:
Firstly, regulations aim to limit the amount of time debris / satellites after the end of their useful lifetimes spend in orbit:
(e) The orbital lifetime of objects passing through LEO (lower than 2,000 km) shall be shorter than 25 years after the end of operation.
(Source: ISO 24113 Debris mitigation requirements and compliance)
Why exactly Inter-Agency Space Debris Coordination Committee (IADC) wants to keep the satellites in orbit after the end of the mission (after all, you would think that it made more sense to take out the trash when the bin gets full, and not after 25 years?) is outlined a bit better by ESA:
A growing number of countries have introduced regulations to limit the production of fresh debris within the protected low orbits, typically intending satellites to be brought down or boosted out of here within 25 years of the end of their working lives while reducing the risk to people on the ground to less than 1 in 10 000.
They also need to be ‘passivated’, removing leftover propellant and powering down batteries to avoid explosions.
So the debris is purposefully kept (for the moment; still deorbited within the planned 25 years) in orbit to try and decommission the satellite to reduce the chance of damage to humans. Also, if you read between the lines, this is done so that there would not be a hail of exploding metal on Earth, which would severely affect both the reputation and funding of space agencies. (An example of this would be to look at how strong opinions the population has towards nuclear power, whilst stating that they don't know it good enough; some might describe nuclear power as "a gift from gods, stomped on out of fear".)
The second issue with prolonged presence of debris is the almost complete lack of opposing forces. In the frame of reference of debris, practically the only constant opposing force is the drag provided by Earth's atmosphere. The atmospherical drag affects everything within about 500 kilometres (about 310 miles or about 1.6 million feet) from the Earth's surface. A document by Cornell University gives the drag mathematically:
For many satellites in low earth orbit (LEO), the largest dynamic model uncertainty stems from atmospheric drag. Acceleration due to atmospheric drag $\boldsymbol{a}_D$ is related to atmospheric density $\rho$ by the equation:
$$
\boldsymbol{a}_D = −\frac{1}{2} \left( C_D \frac{A_v \left( t \right) }{m_s} \right) \rho v_r^2 \boldsymbol{e}_v
$$
where $C_D$ is a drag coefficient, $A_v \left( t \right)$ is the cross-sectional area of the satellite in the direction of travel, $m_s$ is the total spacecraft mass, $v_r$ is the velocity magnitude relative to the ambient atmosphere, and $\boldsymbol{e}_v$ is a unit vector in the relative velocity direction.
From the above formula, we can see that indeed a lower mass object would have a greater atmospherical drag like you suggested. What also plays a major role here is the cross-sectional area $A_v \left( t \right)$ of the debris. If you think about trying to throwing a beachball and a small rock of about equal masses, you know that you can throw the small rock way faster than the beachball, and this is due to the different cross-sectional area $A_v \left( t \right)$ of the two objects.
Now, let's consider entire satellites vs smaller pieces of debris: the smaller piece is probably not hollow, but just a chunk of metal or some composite, where as the satellite will be relatively empty and hollow from the inside. In this case, the ratio between the cross-sectional area $A_v \left( t \right)$ and the total spacecraft mass $m_s$ would be greater for the satellite than it would be for the smaller piece of debris, i.e. the satellite would have a greater drag and deorbit sooner than the smaller piece of debris (assuming the constants and coefficients would stay the same for the two).
This brings into question why did USA and China try blowing up old satellites, creating tens of thousands of new, smaller, longer lasting pieces of debris, when it does not make sense physically?
Long story short, the rate is, sadly, not that high. There are efforts to combat it (see the ESA link above), but so far it is looking pretty horrible on short-term. And to top that, anything above the 500km threshold effectively feels no drag due to the atmosphere. For example, satellites in the geosynchronous orbit (GEO, around 36,000 km / 22,000 mi out) have to be positioned into a graveyard orbit at the end of their lifetime. From Wikipedia:
A graveyard orbit, also called a junk orbit or disposal orbit, is a supersynchronous orbit that lies significantly above synchronous orbit, where spacecraft are intentionally placed at the end of their operational life. It is a measure performed in order to lower the probability of collisions with operational spacecraft and of the generation of additional space debris.
To answer some of your shorter questions:
- This picture from Wikipedia gives some idea how dirty we are:

- Final stage separation is usually designed not to blow off a lot of debris into space, and agencies / launch companies are increasingly trying to bring earlier stages back to Earth (intact or not). Otherwise you may have a piece or two of debris that already has a downwards trajectory on stage separation (Newton's Third Law of Motion: the "extra push" on stage separation affects the earlier stage equally, so while the payload is pushed further away from Earth, the earlier stage is pushed towards Earth.)
- There are about 70-90 launches per year these days, so no, we are not launching orbital payloads at a rate of 1 every 3 days... Merely at a rate of about 1 every 4 days. ;) This does not equate to the number of satellites deployed however: for example, recent developments of CubeSats (tiny (10 cm by 10 cm by 10 cm), cheap satellites) have led to numerous smaller satellites being launched at once along with bigger payload. In late 2013, USAF launched a Minotaur I rocket loaded with its main payload, the Air Force's Space Test Program Satellite-3, and along with it 28 CubeSats, so a single launch deployed an impressive 29 satellites.
So, after all this mumbling, the primary source of space junk really is us. And not really us launching more and more stuff into space, but our lack of progress in effectively removing our past, present, and future orbiters from space after their missions have ended. I hope this helped.
(An obstacle I did not mention is political: governments do not really want to fund missions to remove the space junk. Politicians are much more interested in missions that can "be seen" and credited to their time in government, whereas removing debris would be quite opposite of this (nobody ever thinks highly of the garbageman, despite their infrastructurally important job).)