I recall two definitions from Banach space theory

Definition 1.Let $E$ be a Banach space, then a basis $(e_n)_{n\in\mathbb{N}}$ of $E$ is called $1$-spreading if $$\left\|\sum_{i=1}^k a_i e_{m_i}\right\|\le\left\|\sum_{i=1}^k a_i e_{n_i}\right\|$$ whenever $k$ is a positive integer, $(a_i)_{i=0}^k$ are scalars and $n_1<\ldots<n_k$ and $m_1<\dots < m_k$.

Definition 2.Let $E$ be a Banach space and $(x_n)_{n\in\mathbb{N}}$ a basic sequence of $E$. A spreading model of $(x_n)_{n\in\mathbb{N}}$ is a normalized basic sequence $(y_n)_{n\in\mathbb{N}}$ in a Banach space $F$ such that for every $\epsilon > 0$ and $k\in\mathbb{N}$, there is an $N$ such that $$(1+\epsilon)^{-1}\left\|\sum_{i=1}^k a_i y_i\right\|\le \left\|\sum_{i=1}^k a_i x_{n_i}\right\|\le (1+\epsilon)\left\|\sum_{i=1}^k a_i y_i\right\|$$ for all $N<n_1<\dots<n_k$ and a sequence $(a_i)_{i=1}^k$ of scalars.

Now, looking at these two definitions I get the following:

- If a basis is $1$-spreading then, fixing $n\in\mathbb{N}$, all the subspaces of dimension $n$ generated by a subset of the basis are isometrically isomorphic.
- If $(y_n)\subset F$ is a spreading model of $(x_n)\subset E$ then every finite dimensional subspace generated by a subset of $(y_n)$ is $(1+\epsilon)$-isomorphic to a finite dimensional subspace of $E$.

My two related question, that I supect being almost trivial (I'm relatively new to Banach space theory), are the following:

- If a basis is $1$-spreading then, fixing $n\in\mathbb{N}$, are all subspaces of dimension $n$ isometrically isomorphic? What about infinite dimensional subspaces? Are them all isometrically isomorphic to the space $E$ itself?
- If $(y_n)\subset F$ is a spreading model of $(x_n)\subset E$, is every finite dimensional subspace of $F$ $(1+\epsilon)$-isomorphic to a finite dimensional subspace of $E$? Again what about the infinite dimensional subspaces of $F$?

Thanks!