From the title of your question, the most obvious answer is that the temperature of the planet would be very high due to solar radiation. Based on the rest of your question however, it seems that you are more interested in the gravitational effects on the planet due to tidal forces, so I will focus on those effects.
TL;DR Unless the planet is very close to the star the effects will be small. If it is very close, there can be exreme effects due to tidal heating and tidal locking. Eventually the planet could fall into the star.
Dynamic tidal forces
From the accepted answer to the question you linked, we see that for a planet of radius $r$ orbiting at distance $R$ around a star of mass $M$, the correction to apparent gravitational acceleration due to the tidal force and centripetal acceleration is $$ \Delta a = GM \left( \frac{r}{R(R-r)^2} \right). $$ If the planet has mass $m$, the average surface gravitational acceleration is $$ g = \frac{Gm}{r^2}, $$ so the ratio of the correction due to the star to the averge surface gravity is $$ \alpha = \frac{\Delta a}{g} \ = \frac{M}{m} \left( \frac{r^3}{R(R-r)^2} \right) $$ This can be simplified if we think in terms of the ratio of the radius of the planet to the radius of the orbit $\rho = R/r$, and the ratio of the masses of the star and the planet $\mu = M/m$. This lets us rewrite the equation: $$ \alpha = \frac{\mu}{\rho(\rho - 1)^2} $$
Now let's consider some numbers. For the Earth-Sun system, $\mu = 3.3\times10^{5}$ and $\rho = 2.3\times10^4$, so $\alpha = 2.5\times10^{-8}$ as shown in the linked answer. As you mention in your question, this is a very small effect.
If you want to decrease the orbital period of the Earth to 10 days, we get (from <PERSON>'s third law) that the radius of the orbit has to shrink by a factor of about 11. This means that $\rho$ shrinks by about 11, and $\alpha = 3.4\times10^{-5}$, or about 3 thousandths of a percent. In other words, the tidal forces would still be unnoticible in everyday cicumstances.
If you wanted to continue moving the Earth closer to the sun until the tidal effect was 10% of the normal surface gravity, you would need to have $\rho \approx 150$, which would make the radius of the Earth's orbit about 1 million km, which is a little less than twice the radius of the sun. 24
In other words, for the direct effects of the tidal force to be large, the planet must be extremely close to the star.**
This doesn't mean that there would not be extreme effects on ocean tides, continuous earthquakes, and other geophysical events however. I'm not a geophysicist, but my intuition is the following:
* The ocean tides would be extreme, if there were any liquid water at all. It's possible that all of the water would boil away because:
+ The tidal forces on the earth would result in significant tidal heating, leading to:
+ Large amounts of volcanic activity.
+ Large amounts of seismic activity.
+ Non-trivial contributions to increased surface temperature.
Tidal locking
Note that the energy dissipated by tidal heating comes from the energy stored in the planet's rotation. This means that the planet's rotation will slow down as it loses kinetic energy to tidal heating. Eventually, the planet will become tidally locked. With all the interesting worldbuilding implications that go along with that.
Similarly, there will be tidal heating of the central star. This will have an exremely small effect on the central star, but it can have a large effect on the orbiting planet. The energy for tidally heating the star comes from the orbit of the planet. This means that the planet's orbit will slowly decay until either:
* The star becomes tidally locked to the planet, or
* The planet falls into the sun.
In summary:
* Short term effects are likely to be major, i.e. the planet will survive, but it would likely be uninhabitable due to tidal heating.
* Over the long term, the planet would become tidally locked.
* Over the very long term, the orbit would decay and the planet would end up even closer to the star.
Finally, if the object that the planet is orbiting is any normal star, all of these effects will be small compared to the increased solar radiation. 208