Silicone has a density of ~1.25 g/cm^3 (sources for figures given below), breast tissue ~1.035 g/cm^3, and human fat .94 g/cm^3. For comparison, pure water is 1 g/cm^3. So silicone is definitely not the same density as fat; ih fact, both saline and fat are appreciably less than silicone.
That said, while I wasn't able to find any figures for the viscosity of silicone (or rather, I was; the problem is that silicone can have a wide range of different viscosities), I suspect that the type of silicone used in breast implants has a viscosity much higher than water, creating a "feel" more like fat (which, as it exists in the human body, is semi-solid).
Breast Tissue and SiliconeHuman FatThe dangers of silicone breast implants, provided the surgery is handled well and the implants have appropriate quality control, are very ill-defined, if they exist. Most of the evidence for any risk due to implants is due to epidemiological studies, and the epidemiological studies are far from clear. By its nature, it's much harder to interpret epidemiological results because of the difficulty of controlling for all the variables. That isn't to say it isn't valuable: epidemiological studies formed the beginning of the case against smoking.
The problem with breast implants is that not only are the results from epidemiology unclear, because not all studies showed effects (the typical risk looked for was an increase in autoimmune diseases, though other possibilities were explored), but that supporting evidence is lacking. Animal studies have shown no clear biological effects from silicone. The most serious problem, IMO, is the lack of a plausible mechanism for silicone to produce deleterious health effects. In the case of smoking, some of the carcinogenic effects have been traced to the action of chemicals, typically oxidizers, produced in the combustion. However, silicone is chemically inert, and as far as has been shown, biologically inactive as well. The silicon-oxygen bonds that form in silicone are strong; it's just not a reactive chemical.
In other words, the health risks from silicone implants have been overstated. Implants still can and do rupture, and there are other potential problems related to the interaction of the tissue in the breast with the implant, but silicone is not toxic in any meaningful way.