Why do linearity and constant variance assumptions hold in this case 
So I've been back and forth on whether linearity and constant variance assumptions are satisfied by these plots (for a linear model). What's throwing me off is how in the first plot above we have like a gaussian circle and also the region of highest point density seems to shift upwards (which affects the mean trend line a bit in red).
My professor tells me that these plots do not violate the assumptions as there is no significant change in the y-axis means over the x-axis. Is it really that simple in looking at these kinds of plots? The book we are using says that for linearity we want to see the points bounce randomly around the y=0 in a symmetric way in the first plot. For constant variance, we want to see a vertically uniform distribution of residuals in that plot. And for Scale-Location we just want to see that there is no major upward or downward trend.
Still, something about these plots bother me. I don't quite see linearity and something seems off about saying we have constant variance (move away to the left or right from the center of the cluster and it looks to me that variance starts to compress).
Can someone give me a bit more input and explanation on why linearity and constant variance assumptions hold in this case?
Update
Here is the actual data with the SLR line fitted and the lowess line superimposed:

And adding $\beta_2 x^2$ as suggested:

And $R^2$ goes up from 2.38% to 3.03%.
 A: I am not entirely in agreement about the first plot. Usually, if your lowess fit line shows a pretty clear non-linear trend like this, there could be non-linear relationship between y and any of the x's unaccounted for. And that bending happens at a high data density area makes me feel even stronger about this. You can try compose some "component plus residual plot (URL)" to see which one is the culprit. And try adding a quadratic term of that variable into the model and see if it improves the overall fit.
I do, however, agree that the variance is reasonable. You're correct that in the second figure the dots seem to narrowing down from left to right. But also remember that most variables tend to have fewer extreme values than those closer to its central tendency (think the tails of a normal curve). So, as fitted value goes up, you'd expect fewer cases exist. In real world data a perfectly "block-like" appearance of variance plot seldom exists, unless the outcome is from some distribution like a uniform distribution.
