We study N\'eron models in arithmetic families over regular integral bases of finite type over $S=\Spec\mathbb{Z}$, with $\Spec\mathbb{Z}$ as the basic motivating case. \medskip (1) \emph{Isogeny extension and control of component groups.} Prime-to-residue-characteristic isogenies are controlled on a fixed tame codimension-one locus. Their restrictions to identity components have finite \'etale kernels killed by the isogeny degree, and the induced morphisms on component groups have kernel and cokernel killed by a bounded power of that degree. Consequently, the associated Tamagawa-index defect is bounded in the stated finite-isogeny family. \smallskip (2) \emph{Semicontinuity.} For $p\nmid m$, the function $t\mapsto v_p(\#\Phi_{A,t})$ is upper semicontinuous on a common dense open locus. Across degree-$m$ prime-to-$p$ isogenies, the induced component-group maps have kernel and cokernel killed by $m$; hence their orders divide a bounded power of $m$. \smallskip (3) \emph{Cohomology and conductors.} On the tame locus, the inertia-invariant subspaces of \(H^1_{\et}\) are invariant under prime-to-residue-characteristic isogeny. Since isogenous abelian varieties have isomorphic rational \(\ell\)-adic Tate modules, the Artin conductor exponent itself is unchanged under the isogenies considered here. The component-group estimates in this paper control only the associated local geometric defect terms and Tamagawa-index data. \smallskip (4) \emph{Hecke uniformity.} For integral models of modular curves \(X_0(N)\), after restricting to the dense tame locus where the prime-to-\(p\) Hecke correspondence \(T_\ell\), \(\ell\nmid Np\), extends through genuine prime-to-residue-characteristic isogenies, the induced maps are finite \'etale on identity components and act on component groups with kernel and cokernel annihilated by a bounded power of \(\ell\). Consequently, toric ranks, dimensions of inertia-invariant cohomology, and component-group defect terms are uniformly controlled along the corresponding Hecke orbit on this locus. In the Hodge-type Shimura setting, the analogous statement is conditional on the chosen integral-model and extension hypotheses: the relevant prime-to-\(p\) Hecke correspondence must extend over a dense open as a finite correspondence whose induced maps on the abelian scheme are genuine prime-to-residue-characteristic isogenies with finite \'etale kernels. Under these hypotheses, the same component-group and inertia-invariant cohomology conclusions follow. \smallskip (5) \emph{Heights.} On the semistable locus, for abelian schemes equipped with a fixed symmetric ample line bundle, the line of invariant differentials \(\omega_{A/S}\) enters the standard Arakelov-theoretic decomposition of canonical heights. The paper records compatibility of these local height contributions with the tame geometric data controlled above. It does not claim a new uniform positive lower bound for all non-torsion points in an arbitrary prime-to-\(\Sigma\) isogeny class.