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In 2016, the first strongly lensed Type Ia supernova, iPTF16geu at redshift $z=0.409$ with four resolved images arranged symmetrically around the lens galaxy at $z=0.2163$, was discovered. Here, refined observations of iPTF16geu, including the time delay between images, are used to decrease uncertainties in the lens model, including the the slope of the projected surface density of the lens galaxy, $\Sigma\propto r^{1-\eta}$, and to constrain the universal expansion rate $H_0$. Imaging with HST provides an upper limit on the slope $\eta$, in slight tension with the steeper density profiles indicated by imaging with Keck after iPTF16geu had faded, potentially due to dust extinction not corrected for in host galaxy imaging. Since smaller $\eta$ implies larger magnifications, we take advantage of the standard candle nature of Type Ia supernovae constraining the image magnifications, to obtain an independent constraint of the slope. We find that a smooth lens density fails to explain the iPTF16geu fluxes, regardless of the slope, and additional sub-structure lensing is needed. The total probability for the smooth halo model combined with star microlensing to explain the iPTF16geu image fluxes is maximized at $12\,\%$ for $\eta\sim 1.8$, in excellent agreement with Keck high spatial resolution data, and flatter than an isothermal halo. It also agrees perfectly with independent constraints on the slope from lens velocity dispersion measurements. Combining with the observed time delays between the images, we infer a lower bound on the Hubble constant, $H_0 \gtrsim 40\,{\rm km \ s^{-1} Mpc^{-1}}$ at $68.3\,\%$ confidence level., Comment: 12 pages, 9 figures. Expanded version with improved constraints accepted for publication in MNRAS

We present the best 265 sampled R-band light curves of spectroscopically identified Type Ia supernovae (SNe) from the Palomar Transient Factory (PTF; 2009-2012) survey and the intermediate Palomar Transient Factory (iPTF; 2013-2017). A model-independent light curve template is built from our data-set with the purpose to investigate average properties and diversity in our sample. We searched for multiple populations in the light curve properties using machine learning tools. We also utilised the long history of our light curves, up to 4000 days, to exclude any significant pre- or post- supernova flares. From the shapes of light curves we found the average rise time in the R band to be $16.8^{+0.5}_{-0.6}$ days. Although PTF/iPTF were single-band surveys, by modelling the residuals of the SNe in the Hubble-Lema\^{i}tre diagram, we estimate the average colour excess of our sample to be $ \approx 0.05(2)$ mag and thus the mean corrected peak brightness to be $M_R = -19.02\pm0.02$ $+5 \log( {\rm H}_0 [{\rm km} \cdot{\rm s}^{-1} {\rm Mpc}^{-1}]/70)$ mag with only weakly dependent on light curve shape. The intrinsic scatter is found to be $\sigma_R = 0.186 \pm 0.033$ mag for the redshift range $0.05, Comment: 41 pages, 19 figures, accepted MNRAS